MathDB
Lucky Sevens

Source: AIME 2004 Alt. #14

November 17, 2005
LaTeXmodular arithmetic

Problem Statement

Consider a string of nn 7's, 7777777777\cdots77, into which ++ signs are inserted to produce an arithmetic expression. For example, 7+77+777+7+7=8757+77+777+7+7=875 could be obtained from eight 7's in this way. For how many values of nn is it possible to insert ++ signs so that the resulting expression has value 7000?