The fox and two bear cubs are dividing 100 candies. The fox lays out the candies into three piles; who gets which pile is determined by drawing lots. The fox knows that if the bear cubs get different numbers of candies, they will ask her to equalize their piles, and then she will take the excess for herself. After that, everyone eats the candies they received.

a) Come up with a way for the fox to distribute the candies into piles so that she can eat exactly 80 candies (no more, no less).

b) Can the fox arrange it so that she ends up eating exactly 65 candies?
a) The Fox distributes the candies as follows: 10, 10, and 80. If she gets the pile of 80 candies, the bear cubs will get an equal number of candies, and they won't complain. If she gets the pile of 10 candies, to equalize the portions of the bear cubs, she will have to eat an additional 70 candies.

b) In the end, the bear cubs ate an equal number of candies, so the total number of candies eaten by the bear cubs is even. Since 100 is an even number, the Fox also ate an even number of candies.

## Answer

a) 10, 10, and 80; b) it cannot.