Problem #PRU-78494

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

Problem

Every integer from 1 to 64 is written in an \(8 \times 8\) table. Show 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).