# Brain teaser

I like puzzles that are simple to state and understand. This one is not too difficult.

“There are three boxes. One contains apples. One contains oranges. One contains both apples and oranges.

However, the boxes are mislabeled. One is labeled apples, but contains either oranges or the mix. One is labeled oranges, and contains apples or the mix. And the box labeled Both contains apples or oranges, but not both.

Removing only one piece of fruit from one box, how can you correctly identify all three boxes?”

1. says

I agree, this one really is easy. Remove one fruit from the box that is labelled as “both.” Let’s imagine it is an apple. Thus we can conclude that the box labelled as “oranges” is a mix (because it cannot have only apples). And then the box labelled as “apples” must contain oranges.

2. xohjoh2n says

Most people would have to choose the box labelled “both”.

But Domino could choose any box and still be certain of identifying all three correctly.

3. says

Another simple one:

A jail is overcrowded, so a king decides to give prisoners a chance to escape: “Select a white ball from each of two bags. If you select a black ball from either bag, you will be executed.”

The prisoner is given ten white balls and ten black balls. He can distribute the balls in the bags as he likes, but he must place all twenty balls in the bags, and there must be at least one marble in each bag.

What distribution gives a prisoner the best chance of survival? For example, 5W/5B in each bag is a 25% chance (0.5 * 0.5).

4. Matt G says

0.47638

5. Matt G says

Ack, I mean 0.47368!

6. xohjoh2n says

Well, given the setup was a chance of escape rather than merely avoiding execution, the most logical solution would be to put all the balls in one bag, sock the guard over the head with it, and make off with his keys before he wakes up.

7. Holms says

#3
rot13
Zrgubq 1: Bar juvgr mreb oynpx va ont bar, avar juvgr gra oynpx va ont gjb tvirf gur uvturfg fheiviny punapr, nf tvira ol Zngg T.

Zrgubq 2: Qrpyvar gb cnegvpvcngr. Gur cevfbare erznvaf vapneprengrq, ohg unf n bar uhaqerq creprag punapr bs abg orvat rkrphgrq.

8. John Morales says

FFS, Holms. Boieye meicy diun.

9. Holms says

Cool story, John.