IBM Ponder This #258 · October 2019

Let's assume that Alice and Bob have two (possibly the same) integer amounts of money, uniformly distributed in the [0,99] range with a minimal number of banknotes.
Using the standard US dollar banknotes denominations of 1, 5, 10, 20, and 50, if the set of notes of Alice and Bob is the same - the probability of the amount being the same is about 21%.
Your task, this month, is to find the set of five banknote denominations that uniquely determines the set with the minimal number of notes while maximizing the above probability.

Solution

Best opened after a real attempt

To be added.