MathDB
Two player playing with cards numbered 1~n

Source: 2021 IMOC qualification problem, C3

December 30, 2021
IMOCcombinatorics

Problem Statement

There are n cards on a table numbered from 11 to nn, where nn is an even number. Two people take turns taking away the cards. The first player will always take the card with the largest number on it, but the second player will take a random card. Prove: the probability that the first player takes the card with the number ii is i1n1 \frac{i-1}{n-1}