Chapter 10: Brainteasers 353
Annual returns Every day a trader either makes 50% with
probability 0.6 or loses 50% with probability 0.4. What is
the probability the trader will be ahead at the end of a
year, 260 trading days? Over what number of days does
the trader have the maximum probability of making
money?
(Thanks to Aaron.)
Dice game You start with no money and play a game in
which you throw a dice over and over again. For each
throw, if 1 appears you win $1, if 2 appears you win $2,
etc. but if 6 appears you lose all your money and the
game ends. When is the optimal stopping time and what
are your expected winnings?
(Thanks to ckc226.)
100 kg of berries 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.)
Urban planning There are four towns positioned on the
corners of a square. The towns are to be joined by
a system of roads such that the total road length is
minimized. What is the shape of the road?
(Thanks to quantie.)
Closer to the edge or the centre? You have a square and a ran-
dom variable that picks a random point on the square
with a uniform distribution. What is the probability that
a randomly selected point is closer to the center than
to the edge?
(Thanks to OMD.)