390 Frequently Asked Questions In Quantitative Finance
the first eight days then he knows he can’t be executed
on the last day because of the above, and so he knows
that he must be executed tomorrow, day nine. Therefore
it won’t be a surprise and therefore the execution can’t
happen on the ninth day either. We have ruled out the
last two days, and by working backwards we can rule
out every one of the ten days.
On day four the prisoner is awoken by the executioner,
and hanged. Boy, was he surprised!
Where did our backward induction argument go wrong?
Ok, now I can tell you that this brainteaser is called the
unexpected hangingparadox. There have been many
explanations for why the prisoner’s logic fails. For
example, because the prisoner has concluded that he
can’t be hanged then to surprise him is rather simple.
