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 8×8 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).