5-digit!
Number Theory
Level
3
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.
The answer is 42857.
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1 solution
We can make an 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 (142857 is three times smaller than 428571)