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"
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