**From New Scientist #2749, 27th February 2010** [link]

I invite you to place a digit in each of the nine spaces in a 3 × 3 array so that each digit occurs its own number of times (e.g. if 3 occurs it must occur exactly three times). You can then read eight numbers: three across, three down, and two diagonals read from the top down.

What will be the sum of all the digits used if all these numbers are different and the sum cannot be written using digits from the square?

[enigma1584]

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Make sure you keep the distinction clear between the “digits” and the “numbers”.

The following Python program runs in 481ms to find all possible squares.

Solution:The sum of the digits in the square is 29.