Problem #PRU-107838

Problems Calculus Real numbers Integer and fractional parts. Archimedean property Methods Pigeonhole principle Pigeonhole principle (angles and lengths)
 13–15  3.0

Problem

Consider the powers of the number five: 1, 5, 25, 125, 625, ... We form the sequence of their first digits: 1, 5, 2, 1, 6, ...

Prove that any part of this sequence, written in reverse order, will occur in the sequence of the first digits of the powers of the number two (1, 2, 4, 8, 1, 3, 6, 1, ...).