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 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.

 No Solution Yet Submitted by Ady TZIDON No Rating

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 Analytical Solution (D2?) | Comment 1 of 5
We know the following about N:

a) The 2nd digit must be even, so that it is divisible by 2
b) But the 2nd digit cannot be zero, else the difference of the digits is the same as one of the digits of N
c) The first digit then must be odd, otherwise both digits of N/2 are less than the respective digits in N, so neither can be their sum
d) But the 1st digit cannot be 1, because N/2 has two digits
d) The sum of the digits must be less than 10

Then, the only candidates for N are:

32
34
36
52
54
72

And only 34 works:

N   N/2 Sum of digits of N
32  16  5
34  17  7 -- Only one whose sum is a digit in N/2
36  18  9
52  26  7
54  27  9
72  36  9

 Posted by Steve Herman on 2018-10-25 08:34:16

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