perplexus.info :: Numbers : Difference is sod sum

Difference is sod sum (Posted on 2022-01-28)

Consider all integer pairs (a,b) such that (b-a) = sod(a) + sod(b) (with a < b) Now consider Set A, the set of all possible values for "a", the smaller member of each pair.

Part 1:
Prove that every "a" is a multiple of 9, or find a counterexample.
Part 2: Set M contains every element of Set A divided by 9.
But not every natural number appears in M.
Can you find a pattern to predict which positive integers do not appear in M?

Inspired by a problem on the YouTube channel Dr Peyam Show which asked "Are you smarter than a first grader?" which was itself inspired by Nob Yoshigahara's masterpiece

*** "sod" denotes "sum of digits"

No Solution Yet Submitted by Larry

Rating: 4.0000 (1 votes)

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Any kind of academic help	Katie Thompson	2022-02-18 09:57:25
re: FWIW	Charlie	2022-01-28 22:25:49
FWIQ	Charlie	2022-01-28 22:24:45
part 1 (spoiler)	Steve Herman	2022-01-28 20:28:59

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