A certain brand of candy is sold in boxes containing a specific number, lower than 50, of chocolates--a mix of creams and nut clusters, always the same number of each in each box.

If you choose one candy at a time at random without considering its type (cream or nut cluster), you are four times as likely to have one nut cluster left after eating the last cream as you are to have two nut clusters left after the last cream.

But also, if you were to flip a coin before eating each piece, to decide whether to eat a cream or a nut cluster, and then specifically choose one of those, it would be true that you'd be four times as likely to have X nut clusters left after eating the last cream as you'd be to have X+1 nut clusters left after the last cream, where of course X is a number smaller than the number of nut clusters in the box.

How many of each type are in each such box?

Each such box must contain 30 candies inclusive of 22 creams and 8 nut clusters.

Posted by K Sengupta on 2022-05-13 11:55:02