There are 20 slips of paper in a stack, each with a different number written on it (so 20 unique
numbers). The papers are face down with the numbers concealed. The papers are in no particular order. The
numbers on the papers can be any positive number ranging from small fractions to a googol (1 followed by
a hundred zeroes) or even larger.

You win the game if you manage to guess the largest number among all 20 papers. The game goes as follows.
Turn over one paper at a time and each time you do, you may choose to stop and select the number on the
paper that you

*just turned* as what you believe to be the largest number among all 20 papers. The
CATCH is that you can only ever choose the number on the paper you

*just turned*. If you choose to
keep going and turn over another paper, you cannot choose the number on any previously turned over paper.
And if you turn over all 20 papers, then you MUST choose the number on the last paper.

What strategy do you use to maximize the probability of guessing/choosing the largest number? And what do
you think the probability is of being right?

*Credit: This is a variation of a puzzle created by Martin Gardner in 1960.*