Problem #PRU-60366

Problems Methods Algebraic methods Partitions into pairs and groups; bijections Numeral systems Decimal number system Number Theory Pigeonhole principle Pigeonhole principle (other)
 13–14  4.0

Problem

Prove that amongst any 11 different decimal fractions of infinite length, there will be two whose digits in the same column – 10ths, 100s, 1000s, etc – coincide (are the same) an infinite number of times.