Show that given any \(3\) numbers, there will be two of them so that their difference is an even number.
Show that given \(11\) numbers, there will be at least \(2\) numbers whose difference ends in a zero.
Three whole numbers are marked on a number line. Show that for two of these marked numbers, the point halfway between them is also a whole number.
Show that among any \(51\) whole numbers, all at most \(100\), there must be two that share no prime factors. For example, \(7\) and \(8\) share no prime factors, and the same is true for \(11\) and \(12\).