Problem
COM-B1-M11-P007 Remainders
#7
★★☆☆☆ Level 2 of 5
Prove that among any \(11\) integers, two have a difference divisible by \(10\).
There are only \(10\) residues modulo \(10\).
Group the numbers by their residues modulo \(10\). There are \(10\) residues and \(11\) numbers, so two numbers have the same residue. Their difference is divisible by \(10\).
Standard residue pigeonhole.