Combinatorics counting
Source: 2024 KJMO round 1
October 26, 2024
Combinatorics countingcombinatorics
Problem Statement
Find the number of cases in which one of the numbers 1, 2, 3, 4, and 5 is written at each vertex of an equilateral triangle so that the following conditions are satisfied. (However, the same number is counted as one when rotated, and the same number can be written multiple times.) The product of the two numbers written at each end of the sides of an equilateral triangle is an even number.