## Brainteaser 1712: Squambling

**From The Sunday Times, 9th July 1995** [link]

In “squambling” a number, the first (leftmost) digit is squared, the next is cubed, the next raised to the fourth power, and so on. The total of these answers provides a new number, ready for the squambling to begin again.

For example:

18 → 1² + 8³ = 513 → 5² + 1³ + 3⁴ = 107

107 → 2402 → 100 → 1 → 1 → …If you take my age and squamble it you get a three-figure number. If you then squamble that answer you get my age next year.

How old am I?

This puzzle was included in the book *Brainteasers* (2002, edited by Victor Bryant). The puzzle text above is taken from the book.

[teaser1712]

## Jim Randell 8:38 am

on15 September 2019 Permalink |This Python program runs in 86ms.

Run:[ @repl.it ]Solution:You are 46.We have:

After 91 applications of the function we eventually reach a value of 43, which is stable (i.e.

squamble(43) = 43).The next smallest value at which this occurs is 753:

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