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When positive integer A, which has n digits, is multiplied by (n+2) , the product is a number with (n+1) digits, all of whose digits are (n+1) . How many instances of A exist?

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sqdancefan

Answer:

  A = 95238 (only)

Step-by-step explanation:

The question is equivalent to asking what n-digit number consisting only of the digit n will be divisible by n+1. Of the numbers 1, 22, 333, 4444, ... 999999999, the only one is 666666, which is divisible by 7.

The 5-digit integer A is 666666/7 = 95,238. There is only one instance of A.

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