|a_i - b_i| not all different, when a_i,b_i permutations of 1-7
Source: 1980 Swedish Mathematical Competition p2
March 28, 2021
combinatoricspermutation
Problem Statement
a1, a2, a3, a4, a5, a6, a7 and b1, b2, b3, b4, b5, b6, b7 are two permutations of 1,2,3,4,5,6,7. Show that ∣a1−b1∣, ∣a2−b2∣, ∣a3−b3∣, ∣a4−b4∣, ∣a5−b5∣, ∣a6−b6∣, ∣a7−b7∣ are not all different.