# Sunday Times Teaser 2638 – Digilist

*by Victor Bryant*

I have a list of positive whole numbers in increasing order that use all of the digits 0 to 9 exactly once between them.

The majority of these numbers are prime and the list contains more than one even number.

The final number in the list is a perfect square and is the sum of all the remaining numbers.

What is my list of numbers?

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Slow but it get the job done.

My code version:

Brilliant and ingenious Arthur! But one observer has asked me how it works so I thought it would be nice to document it! So here is my version based on your approach:

My first attempt runs in 8 seconds, yours runs in 0.8 seconds and this one runs in 17 milliseconds. Quite a good overall speed up (around 400) – provided, of course, that my code is free of bugs!