perplexus.info :: Numbers : A number well defined

A number well defined (Posted on 2018-10-25)

Half of my 2-digit number N is also a 2-digit number,
one of its digit being the sum of N's digit, the other their difference.
All 4 digits are different.

Find my number.

See The Solution Submitted by Ady TZIDON

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Algebraic Solution

| Comment 2 of 5 |

Let N = 10a + b

Let N/2 = 10c + d

Then 10a + b = 20c + 2d

c cannot be the sum of the digits, so d = a + b

Then 8a - b = 20c

If c = a - b, then this becomes 19 b = 12a, and the only solution in single digits is (0,0).

So c = b - a.

Then 28a = 21b

4a = 3b

Solution = (3,4)

N = 34 and N/2 = 17. Only solution

Posted by Steve Herman on 2018-10-25 09:33:06

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