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Sunday Times Teaser 3095 – Diddums!

by Brian Gladman on January 14, 2022

by Stephen Hogg

Published Sunday January 16 2022 (link)

“Diddums” was Didi’s dada’s name for numbers where the number of positive DIvisors (including 1 and the number), the number of Digits, and the Digit sUM are equal.

Didi enjoyed mental arithmetic, doing it speedily and accurately. For numbers of digits from 1 to 9 she listed in ascending order all possible numbers whose digit sum equalled the number of digits. Working through her list in order, she quickly found the first two diddums (1 and 11) and the next three diddums. After many further calculations, Didi confirmed that the sixth diddum (which is even) was listed.

“Now I’m bored,” she moaned. “Diddums!” said Didi’s dada.

What is the sixth diddum’s digit sum?

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One Comment Leave one →
  1. Brian Gladman permalink

    This runs in under 40 milliseconds.

    Here is a variation that allows “diddums” with a range of lengths to be output:

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