# Solve these critical thinking puzzles, win a prize!

I love logic puzzles, and a friend showed me some particularly good ones the other day. These are based on puzzles written by the Mathematician from AskAMathematician.com.
If you’re the first to get all three of them correct with correct explanations for all of your answers, you’ll win a prize! Skepticon will send you either 4 Skepticon pint glasses or 6 Skepticon shot glasses. To be eligible for the prize, include the work “banana” in your comment.

And as a bonus just for fun – these questions were from a larger set of 8, and I included the only question I got wrong. Which one did I mess up on?

Question 1: In front of you are four cards. You know that each card has a photo of a famous person on one side, and a photo of an animal on the other. The four sides that are visible to you are as follows: Ken Ham, Richard Dawkins, a narwhal, and a T-Rex. I let you know that all of these cards follow the same rule – that if a card has a religious person on it’s famous person side, it has a dinosaur on its animal side. What’s the lowest number of cards you’d need to flip to determine if this rule is true or false for these cards, and which cards would you flip?

Question 2: Because I’m super nice, I give you a giant one hundred pound watermelon as a gift. You determine that this giant watermelon is ninety-nine percent water by weight. Unfortunately you let the watermelon sit out in the sun, and some water evaporates. Now the watermelon is only ninety-eight percent water by weight. To the nearest pound, what does the watermelon now weigh?

Question 3: While you were at TAM9, you decided to suspend skepticism and gamble – specifically, by playing roulette. But since you want to have some sort of strategy, you decide to flip a coin before each bet to decide whether to place a bet on red or on black (which should have a 50/50 chance of happening). Sadly, you lose sixty seven times in a row – that is, the ball always lands on the opposite color that you pick. If you turned your skepticism back on, it would be most rational to think:

A. You just have shitty luck
B. It’s terrible strategy to flip a coin to pick what color to bet on in roulette
C. You should keep up this strategy because you’ve really likely to win the next bet
D. The roulette table is obviously broken, but you can’t assume that’s intentional
E. The casino or the staff are dirty crooks who have rigged the game against you somehow
F. You can’t reasonably decide which of the listed options are more likely

Good luck!

“Keep posting! Even if someone has already given your response, I’m strongly considering a small consolation prize (for the first 10 correct folks), so it’s in your best interest to post. Unless you don’t like getting special prezzies in the mail, of course. :)”

This is post 10 of 49 of Blogathon. Pledge a donation to the Secular Student Alliance here.

1. says

Good luck, all!As a note, I will be stalking this thread and periodically taking screenshots, so if you’re considering editing your entry… duneventhinkaboutit.

2. Mikesullivan says

Question 1.  Two cards – Ken Ham and the narwhalQuestion 2. 99 poundsQuestion 3.  A. You have shitty luck and, at this, really need a banana.

3. Jimmyrhoffa says

1. Two, ken ham to make sure theres a dino and narwhal to make sure there’s no religious person2. 50 lbs, there was 1 lb of nonwater, 1/(1-.98) 3 E, prob of it happening is 1 in 147,573,952,589,676. Second possibility is D if your coin is broken as well (coin always chooses red, roullette always black)You missed number oneBanana

4. Pyro3d says

1) One, Ken Ham. You didn’t specify that the link went the other way around, so the T-Rex card doesn’t matter. The others could also have dinosaurs, but the rule equally doesn’t apply to them.2) 50 pounds. Since the non-water weight of the watermelon should stay the same, we can equate the 1% with the 2%. Since we can determine that the non-water weight of the watermelon is one pound (1% of 100), we can use that for  2%, and find the weight. 3) B, while the other options are also likely, the face you lose doesn’t guarantee them. (Cue the scene from Rozencrantz and Guildenstern are dead).

5. says

1) 2 cards – Ken Ham and Narwhal. If Ken Ham’s card has a non-dinosaur on the other side, the rule is not true. If the narwhal’s card has a religious person on the other side, the rule is also not true, since a card with a religious person must have a dinosaur. There’s nothing in the rules about the reverse of cards with atheists on, so we can ignore the other two cards.2) 50lbs – At the start 99lb of the watermelon is water and 1lb whatever else watermelons are made of (bananas? I don’t know). After being left out, 100% – 98% = 2% of the melon is that same 1lb of melony stuff, so the whole is 1lb / 0.02 = 50lbs.3) The probability of losing 67 times in a row is one in 2^67, ie about 1 in 147 billion. So this is *extremely* unlikely to be bad luck. If the game is fair, flipping a coin is no worse than any other strategy – there’s no pattern to pick up on. C is for idiots, D might make sense if you were always betting (say) red, but since your choice is random and there’s no sensible way your coin toss can directly affect the wheel, if must be E, and the casino is seeing your bet, then manipulating the wheel (or, at least, it’s far more likely that the casino is crooked than that you’ve lost fairly 67 times on the trot).

6. says

Q1: One card, Ken Ham. You didn’t say that if the famous side ISN’T a religious person, the other side DOESN’T have a dinosaur. So if the Ken Ham card does, the rule fits.Q2: 99 pounds.Q3: You just have shitty luck.

7. Jimmyrhoffa says

8. says

Oh, and I’ll guess you got number 1 wrong, since I seem to remember reading that that sort of puzzle catches a lot of intelligent people out.

9. says

Question 1 is a trick question to prevent banana-wielding creationists from winning. Anyone who embraces mainstream science will know that the categories “famous persons” and “animals” overlap.  :)Question 2: 100 lbs  [You got this one wrong]Question 3: E  (if this is wrong, then the makers of this quiz are dirty crooks who have rigged the game against me somehow)

10. says

And that should have been 1 in 147 billion billion, not 1 in 147 billion.

11. Rob Rogers says

1: 2 cards, Ken Ham and the Narwhal.2: 50 pounds3: Dbanana

12. says

I’m sending you something just for that fucking awesome first response. But everyone else – don’t copy that!

13. DizzyMsIzy says

1. Two cards – Ken Ham and the narwhal – It doesn’t matter what is on the other side of Dawkins card, and there’s nothing saying a non-religious person can’t have dinosaur on the other side2. 50 lbs. – 49 lbs. of water, 1 lb. of melon (the 1. lb doesn’t change)3. A. – You have no reason to believe the casino is purposefully making you lose, the sample size is much to small to make you think this. Your past losing does nothing to alter the probability of any future spin. “Broken” would imply that the roulette wheel somehow knows what you are betting and is meant to let you win some of the time. And the 50/50 chance of coin flip is exactly the same 50/50 of just choosing red or black at random (although always betting on red or black would reduce you chance of losing consistently, but also reduces your chance of winning consistently)banana

14. UrsaMinor says

Banana?  Why would I mention the word ‘banana’? #1:  You would have to flip two cards to test the rule.  If it is true, Ken Ham will have a dinosaur on the reverse, and the narwhal will have a non-religious person on the reverse.  Since there is no rule stating that non-religious people must have any particular theme on the reverse, it is not necessary to turn over the Richard Dawkins and T-Rex cards, because no matter what they have on the reverse sides, they cannot not break the rule.#2 The watermelon weighs 50 lbs after drying  It contains 1 lb of non-water materials at the start, and does not lose anything but water.  If the water content is 98% at the end, then the 1 lb of solids now comprises 2% of the total weight.  Therefore, there are 49 lbs of water left, for a total of 50 lbs.#3  The answer is E.   The probability of being wrong that many times in a row by chance alone, while not zero,  is mind-bogglingly small (two to the minus 67th power).  You weigh the chances of being that incredibly unlucky against the chances that (gasp!) the game may be rigged by humans, and decide that it’s more likely that the casino is cheating.   Note that this answer is only valid for skeptics with some working knowledge of casinos and human behavior.

15. Pyro3d says

face->fact

16. says

Haha, nice try, but it’s not a trick question. I mean non-human animals :P

17. Rob Rogers says

Um, I meant E for #3.

18. Robin says

1. Two, Ken Ham and the Narwhal. The other two cards pass the rule no matter what’s on the other side.2.  50 lb. Completely dry, it would weigh 1 lb.3. Rigging. If it was definitely an ordinary coin and a non-rigged table it’d just be shitty luck, but after 67 times I’d be convinced there was more going on. The question is now, have they rigged the table against me, or am I really able to predict which side will lose from the coin? The former is far more likely. (I considered placing a small bet *against* the usual flow to see if it’s the latter, but if the table is rigged by crooks, they’re probably waiting for me to place a large bet, and that’s much more likely than a magic coin.)Banana.

19. says

What do I win if I point out the winner? ;)

20. says

Keep posting! Even if someone has already given your response, I’m strongly considering a small consolation prize (for the first 10 correct folks), so it’s in your best interest to post. Unless you don’t like getting special prezzies in the mail, of course. :)

21. Sam says

1) Turn over two cards: the religious card, and the narwhal.”If R then D” is equivalent to “If not D then not R”2) 50 lbs1 lb of non-water material is now (100%-98%=2%) of the total weight. 3) F. You don’t have enough information to decide. Losing 67 times in a row would happen 1 in 2^67 streaks, or roughly 1 in 1,000,000,000,000,000,000,000 (one in a hexillion streaks). If one billion people played one trillion times each, we would expect one person to encounter those offs.

22. Question 1.  Two cards, Ken Ham, to see if a dinosaur is on the other side and the narwhal to make sure there’s not a religious person on the other side.  Flipping over the T-Rex is not necessary.Question 2. 50 pounds, or about 180 average-sized skinned bananas.Question 3.  A. You just have shitty luck.

23. Udo says

Question 1 is obviously a trick question: Ken Ham, Richard Dawkins, a narwhal, and a T-Rex are all animals and Ken Ham, Richard Dawkins and the T-Rex are famous (i can’t think of a really famous narwhal; there’s the one from Futurama, the mascot of Ubuntu 11.04 and the one from Weebls Stuff, but neither of those is as famous as the other three animals/persons).

24. Aw man, when I started this no one had posted yet.  :C

25. Sam says

1) Turn over two cards: the religious card, and the narwhal.”If R then D” is equivalent to “If not D then not R”2) 50 lbs1 lb of non-water material is now (100%-98%=2%) of the total weight. 3) F. You don’t have enough information to decide. Losing 67 times in a row would happen 1 in 2^67 streaks, or roughly 1 in 1,000,000,000,000,000,000,000 (one in a hexillion streaks). If one billion people played one trillion times each, we would expect one person to encounter those offs.Banana, even.

26. Anon says

Flipping a coin to choose a colour is worse as it gives a 25% chance of winning. If you have Heads = Red and Tails = Black you have the 4 combinations of HR, HB, TR, and TB giving you less chance that just picking a colour.

27. zyxek says

1) 3 cards- Ken Ham, to confirm dinosaur; Narwhal, to confirm it’s not a religious person; T-Rex, to confirm it’s a religious person.2) 100 lbs. The water evaporated didn’t leave the watermelon.3) The odds of losing 67 times in a row (regardless of method) are miniscule. But if you’re picking different colors, that would exclude the possibility of the table being broken. It is most rational to think that you are being cheated, though these conditions don’t provide empirical proof of that. You would be well within your rights to complain to management and bring attention to the issue. I am guessing no.1 tripped you up. The wording of the question convinces people to pick fewer cards than necessary- in other words, it discourages the collecting of evidence. Banana (I thought there were more ‘n’s)

28. zyxek says

3) E. I got carried away explaining, and forgot to include a letter.

29. Vanessa says

ooh, I love puzzles.1: Two – Ken Ham to make sure there’s a dino on the other side and the narwhal to make sure there’s not a religious person on the other side.2. 50 lbs – The watermelon is now 2% non-water, and because that weight would stay the same (1 lb), .02x=1. x=50.3. A. You must have really shitty luck, because flipping a coin to pick which color is not really a bad strategy, as you have a 50/50 chance of picking the right color anyway.bonus, I think you got #2 wrongbanana

30. Rob Rogers says

The rule for 1 only states “if a card has a religious person on it’s famous person side, it has a dinosaur on its animal side”, without stating the converse. If Ken Ham and the Narwhal confirm the rule, having a non-religious person opposite the T-Rex doesn’t invalidate it.

31. Robin says

Noo! It doesn’t matter which side the coin comes up, because whichever one it does, the table has a 50% chance of matching it.You’re not betting on HR, HB, TR or TB, just R or B.

32. Robin says

And I’m going to guess you missed 3, because that’s the one most people here seem to be getting wrong, unless I am!

33. says

Ah, missed the explanation bit:1) All but the Dawkins card to support true. Flipping Ham to find dino supports true. Flipping dino to find religious person support true. Flipping narwhal to find not religious person to support true. (Dawkins card is exempt from rule).2) 49 bananas of water, 1 banana of watermelon fluff, where 1 banana=1 pound. [100-99lb water = 1lb watermelon fluff. 0.02x= 1lb, x=50 lb.]3) F. (I misread what I meant to type previously, and thought that there were only five options.) ~A (no such thing as luck), ~B (coin tosses are used for 50/50 chance, roulette has a 50/50 chance of color options. This strategy uses a randomized selection and is valid, assuming coin tosses yield 50/50 results over the long run.) ~C (There’s no reason to assume that this strategy is any more likely to flush out the correct answer than a random number table.) ~D (There is a probability of this happening. Each draw has a 50/50 chance, while successive losses build logarithmically and seems “impossible”, there’s no reason to suspect cheating.) ~E (Same reason given as D). Therefore, F

34. says

1: Two. Ken Ham and the narwhal.  You said “if” and not “iff”, therefore the rule holds true even if Dawkins is paired with a dinosaur and the T.Rex is paired with a nonreligious person.2: 50 lbs (the 1 lb that isn’t water is now 2% of the total weight).  Would this work similarly for a banana?3: There’s strong reason to suspect ‘E’, but based on the prompt I can’t rule out the possibility that I am the unluckiest person in the known universe (A). I would need to observe the same phenomenon happening to someone else before I could say that a rigged table is definitely the case. ‘B’ is subjective based on your definition of “terrible”, and it doesn’t hurt your odds any more than picking whichever color you feel like picking. ‘D’ is absurd; the table’s only broken if it fails to operate, or if the ball does not have a 50-50 chance of landing on each color (which it appears to if it is varying at the same rate as your coin toss… unless your coin is broken!). Statistically, ‘C’ would seem correct, but that only holds true if the casino staff aren’t deliberately fucking with you. I don’t have enough info to know for sure, but ‘F’ only specifies which is most likely, so my final answer is ‘E’.

35. James King says

1) One card.To be proved for these four cards is whether creationist front => dinosaur back. The converse isn’t specified as true, mathematically speaking. All you need then is a true premise and a false conclusion to prove it wrong. Only 1 card, Ken Ham, is a creationist, satisfying the premise. Flip it. If it’s a dinosaur, the conclusion is true, if not, it’s false.2) 50 pounds.Let ww = water weight, tw = total weightWe are given that ww / tw = 0.99If some of the water weight evaporates, that decreases the water and total weight by the same amount, x. We then have that:(ww – x) / (tw – x) = 0.98Solving, we find that x = 50 (since we know tw = 100 and ww = 99 from before). Thus after losing 50 pounds, there is 50 lb left.3) A. You have shitty luck.Flipping a coin is no worse than any other strategy, so it can’t be B.C makes no sense whatsoever; the odds should always be 50% and chances of winning do not increase the longer you play.D makes no sense either, since the roulette table can only be broken in a specific, fixed way which should be compensated for by random rolls.E is tempting, but this is a public, non-shady venue and laws are very strict. Casinos already win enough by giving you an HONEST game according to the rules. To cheat so blatantly/obviously would be stupid and would spread word to other players not to try.I say A must then be a bit more likely than the others, so it’s not F. Yes, the odds are extraordinarily long, but still possible. I agree with the 1 in 2^67 figure. You could play a million times and not win even once. I think you’ve got an outlier and the odds should tend to 50/50 eventually with the more games played.Banana.

36. FellBeast says

Banana!1.  Ken Ham and narwhal.  If Ken has a dinosaur and narwhal doesn’t have a religious person, the rule is true.2.  50 pounds.  The 1 pound that isn’t water is now 2% of total weight; 1 is 2% of 50.3.  A.  Using a coin to decide is no worse than just guessing in this case.  Odds are 50/50 either way, so B is wrong.  Previous results don’t affect subsequent attempts, so C is wrong.  D and E have no supporting evidence.  F is wrong because I just did what it says I can’t do.This is my first comment here, by the way.  Hi!

37. says

Mmm. banana. Much better than water mellon.1. Flipping over Dawkins or the T-Rex will tell you nothing about your hypothesis. But you have to flip over Ham to make sure there is a dino, otherwise your hypothesis is falsified. Likewise, if there is a religious person on the other side of the alleged “narwhal” [I’ve never seen one, how do I know they exist?], then your hypothesis would be falsified. Thus you must flip over two.2. This one was fun! Since it started out at 100 lbs. and 99% water, then that means that 1% (or 1 lb) was Not Water (NW). After letting it rot in the sun for a bit (best thing for water mellon, if you ask me), you find that it is 98% water. [BTW, you had to weigh it to figure that out anyway, so why are you asking me how much it weighed?] Well, the 1 lb of NW didn’t change, so that means that 1 lb is 2% of the total weight. That makes the total weight 50 lbs.3. B. It’s terrible strategy to flip a coin to pick what color to bet on in rouletteYou start out with a 50% chance of winning if you bet red every time. But now you are flipping a coin to decide which color to bet. That means that you’ve doubled the population outcomes for yourself, while the wheel is going to plunge ahead hitting red half the time. In other words you went from 50% likely to win, down to 25%. I’d expect you to lose 75% of the time. But please keep playing! My buddy doesn’t understand, and I’m side betting with him that you’ll lose every time! I’m gonna be going home a winner!

38. rob says

Regarding the roulette question, you actually don’t have a fifty fifty chance on red and black because there is a single green slot on the wheel. That’s how the casinos defeat the red or black bets, because you have a slightly less than 50% shot, giving the house a slight advantage.

39. says

Bonus: You got 2 wrong. But if you now reveal to me that you got number 1 right, I’ll change my answer to 3. [Or to 1 if you say you got 3 right!]

40. Robin says

In that scene in Rozencrantz and Guildenstern, they conclude correctly that they are being “held within un-, sub-, or super-natural forces” – in other words, that the table is rigged.

41. says

Mm. Nevermind about my answer for 1. Dino card doesn’t have to have a particular back. So, flip Ham and narwhal.

42. James King says

For (3) I don’t really know much about probability, but I do think the coin toss might be affecting your probability of winning. I’d actually like to change my answer to (B) if possible.My intuition is that the coin is being tossed, and presumably there isn’t anything wrong with it, so in order for the wheel to be contradicting your choice each time, it might be switching between red and black at the same rate as the coin is switching between heads and tails. The outcomes are just mismatched so that it’s coming up red when the coin leads him to bet black, but the wheel itself is probably producing red/black at 50% probability. I was a little hesitant to endorse the long odds from (A), but of the rest it seemed most reasonable. On further thought, (B) sounds better and I didn’t even have a strong argument against it to begin with.If it’s required for all posts to contain “banana”, I’ll put that here too. I didn’t want to edit my post so that you could see it in its original format.Edit: Blah, okay. I noticed my #1 is wrong also. I didn’t really know what a narwhal was so my mind just skipped past it. You’d have to flip that one too to make sure it wasn’t a religious person leading to a false conclusion.Edit2: I’ll also bet you got #3 wrong. Maybe biology people have a better grounding in statistics, but the other 2 just require you to be paying attention.

43. says

1)  All four.  If it happens to be true once, that doesn’t make it true twice. It could have just been chance. If I have the option to take a sample size of all, I’m going to do it.  (otherwise known as ‘MOAR DATA!’)2) 99 pounds. The weight-amount of watermelon ‘meat’ does not change, regardless of what percentage of the watermelon it is. If you lose one percent of a one-hundred pound thing, it becomes 99 pounds. It doesn’t matter how it’s lost.3) E.    There’s no such thing as luck so A is out. Roulette is a terribly strategy with or without a coin flip so no B. The odds are always the same when you’re doing something random, no matter how many times you did it before so C is gone. A broken roulette wheel would not change the fact that you are flipping a coin to determine the color you bet on and a broken wheel wouldn’t change according to your coin flip, so there goes D.  While F might at first seem the most skeptical, the sheer odds of losing a 50/50 chance (And that’s all it is. The coin flip in no way alters the probability of winning.) sixty-seven times in a row makes the house seem highly suspect.Banana!

44. says

What? Really? Damn, my non-gambling habit comes back to haunt me.

45. Azkyroth says

1. two – Ken Ham and the Narwhal.2. 50 lbs.3. F

46. rob says

I used to work in Vegas.  Gambling is my favorite form of math :)

47. says

Trying this again.1) To find as true, 2 cards: Ham (finding dino supports true) and narwhal (finding religious figure supports true). Dawkins and dino are not specifically included in the rule, since it is not defined as if and only if (i.e., athiest figures may have dinos or other animals).To find as false, one card: flipping Ham and finding an aardvark immediately proves the rule false.2) 49 bananas of water, 1 banana of watermelon fluff, where 1 banana=1 pound. [100-99lb water = 1lb watermelon fluff. 0.02x= 1lb, x=50 lb.]3) B Roulette wheels are apparently not divided 50/50 black/red. There’s a green slot, too. Relying on a randomizer that gives you 50/50 odds doesn’t account for the correct probability. This method doesn’t accurately represent the odds and is therefore a bad strategy.(Edited to remove a horrible, awful grammar error of the pluralizing with an apostrophe-s variety.)

48. StephenS says

1)  Two cards – Ken Ham and the narwhal.  The rule says a religious person has to have a dinosaur on its flip side.  Ken Ham is a religious person, so his card has to be flipped to verify the dinosaur on the other side.  Dawkins is not religious, so it doesn’t matter what’s on his flip side.  The narwhal is not a dinosaur, so its card must be flipped to verify that there is no religious person on the other side.  The T-Rex need not be flipped because it doesn’t matter if the person on the other side is religious or not.2)  50 pounds – The watermelon was originally 99 pounds water and 1 pound dehydrated watermelon.  So 0.99 = 99 / (1 + 99).  After evaporation, the relationship is 0.98 = x / (1 + x).  Solving for x we get 49 pounds of water left.  49 + 1 equals 50 pounds.  Incidentally, if that watermelon has been in the sun long enough to evaporate 50 pounds of water, I wouldn’t recommend eating it.  Perhaps, eat a banana, instead.3)  E – Every flip of the coin and every spin of the wheel (unless rigged) are independent random events.  Therefore, B isn’t the case, because any way of choosing roulette bets is equally valid.  C is false because prior history has no effect upon the next spin.  D is false because the broken roulette wheel would have to be producing the same outcome as your coin flips.  That leaves only A and E as possible explanations.  The odds of A, however is so small (I’d guess that lightning striking your car in the parking lot while you’re playing is more likely), that E is the more likely choice.I’ll guess that you got question 1 wrong.  Since, question 2 is just Algebra and question 3 is statistics, I’m guessing you’re unlikely to get them wrong.

49. Chronos Tachyon says

1) The rule is in the form of an if-then, so we need to look for the one combination that would make the rule false (“religious figure” paired with “not a dinosaur”) and fail to find it.  The bare minimum would be one flip: flip Ken Ham and check for a non-dinosaur.  If we had time for a second flip: flip the narwhal and check for a religious figure, e.g. one who makes crazy claims about the intelligently designed banana.2)99% water before: 100 lb watermelon * (1 – 0.99) = 1 lb dry weight.98% water after: x lb watermelon * (1 – 0.98) = 1 lb dry weight.Solve for x: 1 lb / 0.02 = 50 lbs.3)A is possible but really unlikely: ignoring green 0/00, the chances of that happening are 2^-67, or 10^-20.B is false: if the table is fair, flipping a coin makes just as much sense as sticking to one color (there’s no “strategy” for a fair game of chance).C is not just false, it’s a fallacy: if the table is fair, the games have independent probabilities, so the odds of losing the next game are 50:50, just like each of the previous 67.D is possible: depending on how often the ball has been landing in green 0/00, D might be far more likely than A.  However, in the absence of disproportionate green 00 games, it’s not possible for a static table bias to predict your coin flips [EDIT: assuming your coin is fair, naturally].E is possible (for instance, suppose the ball is ferrous, the staff are observing your bets, and the staff are in control of a hidden electromagnet under the table), but the odds are hard to determine without more information.F may be the case, depending on how close the odds are for A, D, or E given the data from the actual games played.Given no further information, E seems to be the most likely possibility, but it depends on your prior for crooked casinos.[EDIT: Oh, and my guess for the missed question: 1, since it’s the most counterintuitive if you haven’t seen a question of that form before.]

50. Robin says

I’m surprised to see this answer to (3) coming up more than once.It’s wrong because you are not betting on something like “heads and red”. Your bet on the table DEPENDS on the outcome of the coin.Suppose you’ve decided to bet on red if the coin comes up heads, and on black if the coin comes up tails. The possible outcomes are:- The coin comes up heads, so you bet on red. The table comes up red. You win.- The coin comes up heads, so you bet on red. The table comes up black. You lose.- The coin comes up tails, so you bet on black. The table comes up red. You lose.- The coin comes up tails, so you bet on black. The table comes up black. You win.In two cases out of four, you win; in two out of four, you lose. 50% chance.(Ignoring the green slot on the table, and assuming a fair coin and a fair table.)

51. MidwayPete says

1. 2 cards. The Ham and the narwhal cards. 2. 50 pounds, as explained above.3. A banana

52. says

banana.1) (assuming that you consider ham a religious person, not a complete charlatan) you need to turn over ham (to verify a dinosaur) and the narwhal (to verify not a religious person). dawkins and the t. rex are irrelevant to the stated rule.2) one percent of the original one hundred pounds is one pound. that one pound is two percent of the postevaporation weight. 1/.02=50. the watermelon now weighs fifty pounds.3) this puzzle is broken, in my opinion. you could argue that d is the best of the given possibilities, but it ignores the possibility that a fellow bettor is gaffing the wheel, perhaps with an electromagnet. indeed, since the ball never landed on green, which maximizes the house edge, you could argue that this is more likely than cheating by the house or the croupier. for the other possibilities,a) luck is bullshit, of course, and hitting .5 to the 67th odds is ridiculously unlucky. way way beyond “shitty”. b) with a slight tinker to allow for the green slots, random chouce is the best strategy, not the worst, for a fair wheel.c) that is the oldest gambler’s fallacy in the book. pascal would be ashamed of it. fair roulette spins are independent trials, and previous results have no effect on the odds of the current spin.e) false. as i showed above, you can reasonably decide that d is the best of the given options.i’m guessing that 3 gave you problems, since the other two are so trivial.

53. Bryn Dickinson says

54. Robin says

Wait… question 1: *if you got lucky* it would sometimes be possible to falsify the rule after one card flip – say if you flipped the narwhal and got the Pope. Are you asking for the minimum amount in any circumstances? Do you have to flip both the cards before looking at either? Is the question ambiguous, or did I just miss the point?

55. says

1. 1 is the lowest number that I need to flip, provided that the card I flip does not adhere to the rule (flip Ken Ham or the narwal).  This of course depends on the assumption that the statement “- that if a card has a religious person on it’s famous person side, it has a dinosaur on its animal side”  is all true or all false.  If the statement can be all true OR can be partially true, then 2 cards are necessary as described in many posts above (those two cards are Ham and narwhal).2. 50 lbs.  For 1% non water weigh to change to 2% non water weight, with only the water weight in flux, then half the original weight must be present3.  B.  In American roulette betting even/odd or red/black gives a 47% chance of winning.  However, by flipping a coin before the bet is placed, you are DRASTICALLY decreasing your odds of winning.  By betting just red/black you are getting 47%, but by introducing the coin flip you are betting that two random events line up (.5*.47) resulting in a measly 24% (.236) chance of winning per roll.  So while going o for 67 is certainly unlucky, the probability states that out of 100 turns, 77 should be expected to lose.  Banana4.  The roulette problem was likely your downfall.  Probability problems suck.

56. ckitching says

Well, for 3, the game of roulette is by-definition rigged.  The zeros that appear on the board don’t belong to either betting color, so even if you weren’t getting 67 losses in a row, you’d most likely still be losing.

57. Jared says

To begin with, the banana was obviously designed for the human hand.1. Two cards: Ken Ham and narwhal2. 50 pounds3. E: The only choices that can’t be eliminated right off the bat are A, E, and F; and the probability of rigging has to be vastly greater than 2^-67 so that’s sufficient evidence to assume E.Bonus: I’ll guess you missed 1 since a lot of people get that wrong.

58. Bryn Dickinson says

Going with an equal-probability roulette table, there are four equally likely outcomes:Coin chooses red, roulette is red: WINCoin chooses black, roulette is red: LOSECoin chooses red, roulette is black: LOSECoin chooses black, roulette is red: WINI think winning is still 50% if you choose by coin.

59. Garrett Severson says

60. zyxek says

Yeah, I realized that about an hour after submitting my answer. I over-think logic puzzles all the time. This is the first one I’ve tried in a couple of years.

61. Ross says

1) You would have to flip over two cards (Ken Ham and the narwhal). Ken Ham to make sure there’s a dinosaur on the back, and the narwhal to make sure there isn’t a religious person on the back. The others don’t matter.2) 50 lbs. 1% of 100 lbs is 1 lb of non-water, and if 1 lb of non-water is then equal to 2% of the total weight, multiply by 50 to find the total weight.3) E. The coin flip doesn’t make a difference, since there’s still a 50% chance of the roulette table matching your bet. The chances of legitimately losing a 50-50 bet 67 times in a row are so abysmally small that they can effectively be ignored. Assuming the coin didn’t produce the same result for all 67 flips (which has the same abysmally small chance of happening as legitimately losing 67 times in a row), the table would have produced at least some red and some black spins, which indicates either a normal table or one that is intentionally rigged. The chances of the table being legitimate have already been shown to be effectively 0, so the most likely option is that the casino has rigged the table against you.By the way, did you know bananas were designed to fit perfectly into the human hand?

62. Ross says

I forgot to guess which one you got wrong. My guess would be A, since the others are just math.

63. Ross says

Make that A a 1. I spent a lot of time typing the answer to number 3 and got the letter system imprinted in my mind.

64. says

1. Ken Ham, to make sure there’s a dinosaur on the other side, and the narwhal to make sure there isn’t a religious person. Flipping over Dawkins and the T-Rex is unnecessary because the rule could still be true regardless of what’s on the other side. I could explain this better with a truth table for the “implies” sign, but I think this is enough.I’m guessing this is the one you got wrong.2. The watermelon now ways 50 pounds. The part of the watermelon that wasn’t water weighs 1% of 100 pounds, which is 2% of 50 pounds.3. B & C are right out, those are well known fallacies. If the table is broken such that it always turns up the same colour, that wouldn’t explain anything unless the coin is also fixed. But I think you’d notice if you were betting on black every single time and red came up every single time. I don’t think there’s any way it could be broken in a way that would cause 67 losses in a row.So either it’s shitty luck, or someone is controlling the roulette table to make you lose. If you make one bet a minute, it would take roughly the age of the universe to get 67 losses in a row. So my money’s on E.Also banana.

65. Scott says

1) 2 cards – For the rule to hold true, the Ken Ham card must have a dinosaur (modus tollens) and the narwhal card must have a non-religioso (modus tollens).2) 50 lbs. – If the 100 lb watermelon is 99% water, then 1 lb is not water. Now with some of the water gone, that 1 lb of non-water is now 2% of the weight. Therefore, 50 lbs.3) You have a 0.5 probability of winning any given spin (actually, slightly less if there are 1 or more “0” slots on the wheel). So, to lose 67 times in a row would be a 1 in 2^67 longshot at best. Statistically speaking, any occurrance with a 0.05 probabilty of happening by chance is considered to be “statistically significant”. This occurance is far below that threshold. A broken table shouldn’t matter (unless, as a previous poster mentioned, the coin is also broken, or unless the table is broken to always land on one of the “0” slots). So no matter how srtrict the laws regulating gambling are enforced (they can never be 100% due to human error), there is still a far greater chance that the casino is cheating, as opposed to the next most reasonable option (the wheel AND the coin are “broken” or the wheel is broken to always land on a “0” slot), and the distant third place option (shitty luck). The most rational choice is F.

66. Scott says

If the water didn’t leave the watermelon, then how is it now only 98% of the weight? ;)

67. Scott says

Bonus: You got #3 wrong.

68. says

Since I’ve seen the right answer for the first two a half dozen times (Ken Ham & narwhal; 50 lbs), I’m curious as to the logic behind the 3rd question. Here’s mine. Banana banana banana terracotta pie!Let’s look at this scientifically. Let’s take alpha = 5% level of significance. The null hypothesis is that the roulette wheel is truly random. A further assumption is that your coin is fair: it gives heads / tails at a 1:1 ratio. Finally, we assume that the coin and roulette wheel are independent.As discussed above, the probability that the coin correctly predicts the outcome of the roulette wheel is 50% (let’s disregard the 0 and 00 slots). Then again, as discussed above, the probability of exactly 0 correct predictions is choose(67, 0) * pow(1/2, 0) * pow(1/2, 67)  = 1/2^67.Thus the probability that this occurs due to random chance (i.e. the probability that the null hypothesis is correct) is 1/2^67, or MUCH lower than 5%. Thus we would reject the null hypothesis.So the alternate hypothesis is that the roulette wheel isn’t random. Or more particularly, the roulette wheel is *not* independent of the coin flip. Thus, without any further information, I would assume that the table operators are somehow cheating. That being said, I would run some clandestine experiments to see if I can somehow prove this.

69. David Byars says

Question 1: 2. Ken Ham, and a narwhal. You are trying to disprove if a card has a religious person on it’s famous person side, it has a dinosaur on its animal side. But a nonreligious person could still have a dinosaur, so the dino and Dawkins are irrelevant (as well as irreverent, in the latter case) Whereas Ham’s reverse being a non dino or the narwhal having a religious person (like Banana Man) as its backside would disprove the notion.Question 2: To the nearest pound, what does the watermelon now weigh? 50 pounds.At first, 99% water weight is 99 lbs. 1 lb non water weight for 1%. 100 lbs total.1/1%=100After, 98% water weight, 1 lb non water weight for 2%.1/2%=50 lbs totalQuestion 3: F. You can’t reasonably decide which of the listed options are more likelyA. You can’t expect to win 50%B. It’s a random generator, so flipping a coin works as well (badly) as any other strategyC. Failing previous rolls doesn’t make the same strategy more likely in the futureD. No reason to think it is brokenE. No reason to suspect fraudso, F. You can’t reasonably decide which of the listed options are more likely

70. Ira Hanson says

1. Ken Ham, Narwhal2. 50 lbs3. E

71. says

#1 – 2 cards, Ken Hamm & the narwhal#2 – watermelon weighs 50 pounds#3 –  First off, though, ‘most rational’ is too open-ended a criteria, unless you means it satisfies Occam’s Razor (i.e., requires fewest assumptions). I want to say F, but possibly my answer is E, depending on a definition of the word “luck” in option AAt any rate my answert depends on what the word “luck” means. Does it refer to an intrinsic quality of myself that made it more likely that I was the one to experience this event, as opposed to any other rando? If so, then I answer E, the people are cheating, no evidence that an individual can alter the probability of events happening (apart from interfering, in this case with the ball/spin).if “luck” just means that I witnessed a crazy rare event because, well, someone had to, and I am applying the term “luck” to emphasize how unlikely it felt, then I would answer F, can’t decide.Flipping a coin is an irrelevant strategy, there is a 1/4 chance on any spin (minus odds it hits 0/00) that spin & coin-flip match up. This is same odds for the strategy of always choosing red or black, coin flip should be no different than just choosing one or the other, in any case there is a 1/2 odds you choose black, 1/2 ball lands black, 1/4 you choose correctly (minus odds of 0/00 hitting).based on my iPhone calculator (which is really based on what little I remember of long-aso math skills), the odds that you lose every hand are on the order of 4 x 10^-9 (.76^67), so like 4 in a billion? Those are actually pretty good odds, all things considered and given several decades of roullette games. So I wouldn’t know if I was being cheated or if this was just some fluke event,Is there a better than 4 in a billion chance casinos are cheating me? Whew, I tend to think Nevada is pretty serious about their regulation of casinos, but this impression is based mostly on the film Ocean’s 11, so that hardly counts. And regulating bodies are made of people, so that leaves room for error or corruption, both extremely common-place characteristics of people & their institutions. So I think it is too hard for me to tell how likely the odds of a cheatign casino are, maybe it is just a lack of info, but that is what I am working with

72. Scott says

Ugh. I meant (as my explanation shows) that the most rational choice is E.

73. Leo Buzalsky says

1.   Two cards.  The Ken Ham card is fairly obvious.  We need to make sure a dinosaur is on the other side.  The other card is the narwhal.  We need to make sure the other side is NOT a religious person.We do not need to flip the Richard Dawkins card as he is not religious.  We also do not need to flip the T-Rex card, as the rule only works one way.  In other words, the rule does not state that a dinosaur card will have a religious person on the other side.2. The watermelon now weighs 50 pounds.  Initially, the watermelon was 99 lbs water, 1 lbs other.  The watermelon still has that 1 lbs of other weight.  Let x = water weight and t = total weightx/t * 100 = 98%Substitute in (x+1) for t.x/(x+1) = 0.98  –>  x = 0.98 (x + 1)  –> x – 0.98x = 0.98 –? 0.02x = 0.98  –> x = 0.98 / 0.02  –> x = 49Now, remember, x is just the water weight.  We still need to add in that 1 lbs of other weight.49 + 1 = 50 lbs.3.  I have to say the answer is B.  It is a bad strategy to flip a coin.  There is a 50/50 chance of getting a certain color, but there is also a 50/50 chance of getting a certain coin flip.  The probability that your coin flip matches the roulette color is 1/2 * 1/2 = 1/4.  By adding in the coin flip, you have effectively reduced the probability of getting the desired result by 1/2.  Now, going back to that 1/4 probability, if you play 67 times, you would expect to get the desired result 67 * 1/4 = 16.75 (16 after rounding down) times.  It would seem that there is some “shitty luck” here (making A look like reasonable answer), until you consider, using your skepticism, that probability is not a guarantee of the outcome.  (To clarify, just because probability predicts that the desired result should happen 16 times, we know that it does not have to, and this is where we get this absurd notion of “luck”.)I now need a banana to rejuvenate from this mental exercise.

74. MidwayPete says

So, are we going to get an official ruling about the answers?

75. says

76. Spgcell says

Ken Ham, narwhal, 50, banana.Why is the coin toss included in problem 3? It is necessary to establish two things: that you the bettor are switching randomly between red and black; and that the roulette wheel is also switching between red and black, and always the opposite color from the one you bet on (never green). That means the wheel is not broken, it is rigged.Imagine the following sequence: you bet 7 times, and lose all 7.  Suspecting something, you decide to keep track for 30 bets, starting with the 8th bet. As the ball drops for the 30th time in the opposite color from your bet, you realize that the odds of that happening are about 1 in a billion.Astonished, you hail James Randi, and explain what has happened. He says that is extremely unlikely, and then asks the skeptic’s question: is that reproducible?So with Randi sitting at your side, you then do another 30 bets,  again switching randomly between red and black based on your coin toss. Once again, the ball drops in the opposite color of your bet each and every time. You look over at Randi to see what he thinks, and he has just one word to say:”Rigged.”

77. Cripdyke says

Ken Ham – a total of ONE card flipped50 poundsE – the game is riggedBonus: You got the watermelon’s weight wrong

78. Cripdyke says

it’s too late, but I realize now that you would have to flip TWO cards, Ken Ham & the Narwhal. Frack.

79. Spgcell says

As a comparison to the long odds of losing on red or black 67 times in a row, you are at least 25 times more likely to win the Powerball Jackpot twice in a row.

80. Frank says

Flip 2 cards: Ken Ham and narwhal. Theonly way the rule can be violated is if a card has a religious personand a non-dinosaur. Richard Dawkins is not a religious person, and aT-Rex is a dinosaur, so neither of those cards could possibly violatethe rule. If the Ken Ham card has a non-dinosaur, or the narwhal cardhas a religious person, then the rule is violated, so both of thosecards need to be checked.50 pounds. Before it had 99 pounds ofwater and 1 pound of non-water. Now it still has 1 pound ofnon-water, which accounts for 2% of its weight. 2% * x pounds = 1pound, divide both sides by 2% and we have x pounds = 1 pound / 0.02= 50 pounds.E, by process of elimination. It’s notA, because the probability of loosing 67 coin flips is 2^-67, whichis less than 10^-20. In the entire history of humans gambling, almostcertainly nobody has had luck that is that bad. It’s not B, becauseflipping a coin is no better or worse than any other method ofdeciding what to bet on. It’s not C, because the chances of winningthe next round have nothing to do with how many rounds one has justlost. There is no magic ledger of luck that makes sure that people ona loosing streak start winning. It’s not D, because there is no way atable can be broken in just such a way as to always go against a cointhat it isn’t interacting with. All that leaves is E.

81. says

But, you forget to factor in that I was drinking!

82. says

However, if there is a religious person on the Narwhal card it would disprove the rule.

Where are you, answeeeeeers? I would have thought you have to turn over 3 cards (Ham, Dawkins, Narwhal).   Because the Dawkins side we’re seeing could actually be the Animal side of a card, not the Famous Person side.  For all we know, Fred Phelps could be lurking under Dawkins.The watermelon now weighs 50 pounds.  1 pound of non-water mass with the new 98% water ratio gives 50 total.And for question 3, I would never gamble.  I’m far too cheap.  But presuming someone spiked my banana-tini, I would have to go with Option E.  I can’t say they’re for sure cheating me, but it’s probably a reasonable enough assumption that it’s time for me to get back to my banana-tinis.

84. UrsaMinor says

And on the off chance that I won a prize, it will have to wait until I get back from vacation in a couple of weeks.