Sunday Times Teaser 3095 – Diddums!
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?