# Answers to the critical thinking puzzles

Many of you took a shot at answering the critical thinking puzzles I posted during Blogathon. Now it’s time for the answers! And because I’m lazy, I’m just going to copy and paste the explanations given by some of you guys!

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?

Answer from UrsaMinor: “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.”

Alternative smartass answer from James F. McGrath: “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: 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?

Answer from Gary Usleaman: “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.”

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

Answer from Jonathan: “The probability of losing 67 times in a row is one in 2^67, ie about 1 in 147 billion 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).”

Katie was nice enough to make up some graphs of your responses:

Most of you guessed I would fail at the door question, followed by the roulette question… But I actually got the watermelon question wrong. I know, I know. The answer is obvious now that I see it, but I’m rusty and wasn’t thinking. Alas.

Congrats to our winner, Jimmyrhoffa, who was the first to get all of these right! Katie should have your prize to you soon.

1. OverlappingMagisteria says

I think I must’ve got both the door question and pineapple question wrong, because I have no recollection of doing them at all

2. Rishi says

Hey!! I got all the answers right too, only I didnt post them. Shouldnt I be getting a prize as well? I can give you the right answers if you want them now.Here 1) Ken Ham and Narhwal2) 50 lbs3) Option ESo where’s my prize?

3. Rishi says

I meant got them right before everyone else.

4. Rishi says

Oh, bananas.And here are the explanations :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.Or 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. :)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) The probability of losing 67 times in a row is one in 2^67, ie about 1 in 147 billion 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.There.Also you got the, uuuh, lemme see, second one wrong? Right?( Stop me if / when this starts to sound lame NOT cuz you cant ahahaha.Huh? Name? Its Rishi and I….. Oh Lame, you said Lame. OK yeah….yeah I know, Lame )

5. says

The REAL answer is don’t send Katie fruit shopping, because she doesn’t know the difference between watermelons and pineapples…

6. NotThatGreg says

I also got the watermelon one wrong; I ‘skipped’ the card one ( too lazy; still want to have a look at it) and I got the gambling one right (I would also add that (a) the crooks fixing the wheel really don’t  understand the psychology of the situation, and won’t be in business long even if not actually busted; and (b) wouldn’t you notice after 10 or 20 ??  67?? Damn).Yeah, I figured the watermelon started off at 99 lbs water, 1 lb not,  if it dried to 98 lbs water, 1 lb not, that seems awfully close to 98% water (Doh, wrong, still very close to 99%). Didn’t seem tricky enough to think about it any more  (Doh, wrong).

7. says

I’m still on the fence about the roulette question. I don’t know how you’d quantify the chances of E – cheating at roulette means the croupier and the casino risk bad publicity, getting sued, criminal proceedings, and ultimately loss of revenue.If this were some sketchy back alley roulette game, I’d say E all the way. But a big name Vegas casino has too much at stake to allow that to just happen. And I don’t know how you’d work out their willingness to take that risk, in order to compare it against the 2^-67.

8. says

It seems like ‘bad luck’ should be a reasonable answer for the roulette question, as the question did open with “you decided to suspend skepticism”.

9. NotThatGreg says

Ah … Bayesian analysis. Still, it does seem pretty hard to overcome the 2^-67. How about G: God exists, is all-powerful, and all-seeing, and hates you and wants you to always lose at roulette.

10. says

My “prize” is that one of my answers got highlighted! And I get to watch a water mellon rot in the sun. Shrivel, Evil Fruit of Satan! Shrivel!

11. Rieux says

This came up on the earlier thread, but the entire roulette question depends upon a conception of roulette that’s simply false. As a handful of commenters noted back there, there aren’t two colors on a roulette wheel, there are three—red, black, and green. As a result, the line “you lose sixty seven times in a row – that is, the ball always lands on the opposite color that you pick” doesn’t make any sense: in a universe of three colors, there is no such thing as an “opposite color.” Whoever wrote that question hasn’t spent much time playing roulette.Possibly there’s a similar information failure in the parenthetical phrase “which should have a 50/50 chance of happening”; conceivably the question-writer meant that to describe the odds of red vs. black winning (which, as noted, is false to fact regarding roulette at any Vegas casino), but the way it’s inserted into that paragraph, the phrase actually describes the likelihood that the subject will bet on red vs. black. I.e., the coin is fair. (And that’s bascially a red herring with regard to the actual math problem, which implies that the whole parenthetical phrase may be a misplaced modifier.)Anyway: there being no such thing as an “opposite color” in a red-black-green universe, we’re left with the coin-flip-chosen color simply losing 67 times in a row. Which is, indeed, awfully convincing evidence of a rigged game—unless the wheel is broken in a very simple way: green always wins. In that case, you can flip your red/black coin as many times as you’d like; regardless, you’re never going to collect from that wheel. So we can’t actually choose between D and E unless we have an additional piece of information not provided in the question—one that an actual roulette player in this situation would obviously be privy to.If green has won 67 times in a row, then probably D, though you can’t exclude E (and how dumb are you for not even once abandoning the stupid coin and betting on green, if for no other reason than to see if anything changed?). So arguably F in this case, but the “you can’t assume that’s intentional” in D seems closest to the mark.If, instead, the results have been a reasonable mix of reds, blacks, and the rare green, with the only consistent tendency that all 67 have been losers for you and your coin, then sure: E. Still, though, in that (very likely) case, Jonathan’s math is wrong. A fair Vegas-style roulette wheel doesn’t give a red/black bet a 1 in 2 chance of losing, as he presumes; it gives that bet a 20 in 38 chance (a.k.a. a 1 in 1.9 chance) of losing. So the proper computation is 1.9^67 (≈ 4.7 x 10^18). That number is actually only about 3% of the size of Jonathan’s result (2^67 ≈ 1.5 x 10^20), so by that (arguably misleading) measure 2^67 is a fairly large error. Of course, 1.9^67 is still absurdly high and clearly more than unlikely enough for cheating to be by far the best explanation.

12. Rieux says

Meanwhile, Disqus’ utter disregard for all my paragraph breaks is… guh.