Problem #PRU-78494

Problems Number Theory Divisibility Division with remainders. Arithmetic of remainders Division with remainder Methods Pigeonhole principle Pigeonhole principle (other)

Problem

Every integer from 1 to 64 is written in an \(8 \times 8\) table. Prove that no matter the order these numbers are written, there are two adjacent numbers which are at least \(5\) apart. (Numbers in cells which share a side are called adjacent).