The Puzzle: What 5-digit number has the following features:

If we put the numeral 1 at the beginning, we get a number three times smaller than if we put the numeral 1 at the end of the number.


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The Solution . . .

Using an easy equation: 3(100000 + x) = 10x+1 (Why? Well, adding 100000 puts a 1 at the front of a five-digit number, and multiplying by 10 and adding 1 puts a 1 at the end of a number) Solving this gives: 10x+1 = 3(100000 + x) 10x+1 = 300000 + 3x 10x = 299999 + 3x 7x = 299999 x= 299999/7 = 42857 The answer is 42857.