perplexus.info :: Just Math : Recover a number

Recover a number (Posted on 2019-10-29)

A certain positive integer N is twice the product of its digits.

Find N.

See The Solution Submitted by Ady TZIDON

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by hand

| Comment 2 of 6 |

For N=3 digits, 100a +10b +c = 2(a + b + c)

or 98a + 8b = c which requires a=0. A larger value of N is similarly ruled out.

So 10a + b = 2a + 2b, 8a = b.

Then a=1, b=8, and N=18 = 2(1+8).

Posted by xdog on 2019-10-29 12:01:05

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