Erasing random numbers on a blackboard
Source: ICMC 2023 Round 2 P3
March 1, 2023
ICMCcollege contestsprobabilitycombinatoricsrandom process
Problem Statement
The numbers are written on a blackboard and then erased via the following process:
[*] Before any numbers are erased, a pair of numbers is chosen uniformly at random and circled.
[*] Each minute for the next minutes, a pair of numbers still on the blackboard is chosen uniformly at random and the smaller one is erased.
[*] In minute , the last number is erased.What is the probability that the smaller circled number is erased before the larger?Proposed by Ethan Tan