Chapter 10: Brainteasers 371
Solution
Suppose you have won an amountSso far and you
have to decide whether to continue. If you roll again
you have an expected winnings on the next throw of
1
6× 1 +1
6× 2 +1
6× 3 +1
6× 4 +1
6× 5 −1
6×S=15 −S
6.So as long as you have less than 15 you would continue.
The expected winnings is harder.
You will stop at 15, 16, 17, 18 and 19. You can’t get to
20 because that would mean playing when you have 15,
and throwing a five. So we must calculate the probabili-
ties of reaching each of these numbers without throwing
a six. At this point we defer to our good friend Excel.
A simple simulation of the optimal strategy yields an
expected value for this game of $6.18.
100kgofberries
You have 100 kg of berries. Ninety-nine percent of
the weight of berries is water. Time passes and some
amount of water evaporates, so our berries are now
98% water. What is the weight of berries now?
Do this one in your head.
(Thanks to NoDoubts.)
Solution
The unexpected, yet correct, answer is 50 kg. It seems
like a tiny amount of water has evaporated so how can
the weight have changed that much?
There is clearly 1 kg of solid matter in the berries. If
that makes up two percent (100 less 98%) then the total
weight must be 50 kg.