# Sunday Times Teaser 3099 – Recurring Theme

*by Andrew Skidmore*

#### Published Sunday February 13 2022 (link)

Liam is learning about fractions and decimals. He has been shown that some fractions give rise to decimals with a recurring pattern eg 4/11 = 0.3636… . Each pupil in his class has been given four numbers. The largest (two-figure) number is to be used as the denominator and the others as numerators, to create three fractions that are to be expressed as decimals. Liam found that each decimal was of the form 0.abcabc…, with the same digits but in different orders.

Liamâ€™s largest number contained the digit 7 and if I told you how many of his four numbers were divisible by ten you should be able to work out the numbers.

What, in increasing order, are the four numbers?

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Nested dictionaries! Witchcraft!

Below is a study I did on your solution, dialling back the sophistication to help my understanding of your code.