# Sunday Times Teaser 2821 – Magic Cards

*by Andrew Skidmore*

#### Published: 16 October 2016 (link)

Joe placed nine cards on the table to form the magic square shown on the left below (where each row, column and diagonal has the same total). Then he turned over each card one at a time and the result is shown on the right below: it is not magic.

__________ |
4 |
11 |
9 |
__________ |
7 |
4 |
8 |

13 |
8 |
3 |
3 |
6 |
9 |
||

7 |
5 |
12 |
2 |
14 |
1 |

Penny then rearranged the cards to form a magic square which, after each card was turned over, was also magic.

What (in increasing order) were the four corner numbers in her magic square with the higher total?

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There are far faster ways of checking whether a 3 by 3 grid of numbers forms a magic square than the approach I have used here but this gets the job done in less than a second.

Here is a much faster version:

Here’s my programmed solution. It runs in 43ms.

It uses a couple of utility routines from the

enigma.pylibrary – available at [ https://www.magwag.plus.com/jim/enigma.html ].