Question 14
Consider a string of $n$ $7$’s, $7777\ldots77,$ into which $+$ signs are inserted to produce an arithmetic expression. For example, $7 + 77 + 777 + 7 + 7 = 875$ could be obtained from eight $7$’s in this way. For how many values of $n$ is it possible to insert $+$ signs so that the resulting expression has value $7000?$