perplexus.info :: Numbers : Pandigital pattern

Pandigital pattern (Posted on 2016-06-28)

Find all pandigital sums of the form
abc+def=ghi
(with no zero) in ascending order of ghi and find a pattern in these sums.

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Mod 9

Comment 2 of 2 |

Pattern aside, all pandigital sums must be evenly divisible by 9.

This is because x + y + z = 0 mod 9 if all digits 1-9 are represented in x, y and z exactly once.

But if x + y = z mod 9,

then x + y - z = 0 mod 9,

so 2z = 0 mod 9,

so z = 0 mod 9.

Edited on June 28, 2016, 8:11 pm

Posted by Steve Herman on 2016-06-28 10:29:32

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