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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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:

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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