decimal fractions of 1/k!
Source: All-Russian 2007
May 4, 2007
number theory unsolvednumber theory
Problem Statement
Dima has written number on infinite pieces of papers as decimal fractions (the following is written on the last piece: \frac {1}{99!} \equal{} 0{,}{00\dots 00}10715\dots, 155 0-s before 1). Sasha wants to cut a fragment of consecutive digits from one of pieces without the comma. For which maximal he may do it so that Dima may not guess, from which piece Sasha has cut his fragment?
A. Golovanov