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25k if beheaded (Posted on 2015-01-01) Difficulty: 3 of 5
List all positive integers such that deleting their first digit is equal to dividing the number by 25.

See The Solution Submitted by Ady TZIDON    
Rating: 3.0000 (1 votes)

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Solution Answers (no explanation | Comment 1 of 3
Let the number be n digits long, with a body of b (length n-1) and an initial digit of a.

Then a*10^N-1 + b = 25b

b = a*10^n-1 / 24 = 125*(a/3)*10^(n-4)

In order for b to be an integer, a must be a multiple of 3. and n must be at least 4.

So a can be 3, 6, or 9.

Each leads directly to a solution

The full number = 3125*10^k or 6250*10^k or 9375*10^k

  Posted by Steve Herman on 2015-01-01 19:00:08
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