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Calendar Capers

Choose any three by three square of dates on a calendar page. Circle any number on the top row, put a line through the other numbers that are in the same row and column as your circled number. Repeat this for a number of your choice from the second row. You should now have just one number left on the bottom row, circle it. Find the total for the three numbers circled. Compare this total with the number in the centre of the square. What do you find? Can you explain why this happens?

Different Magic Square

Stage: 3 Short Challenge Level: Challenge Level:1

The numbers $13$, $10$ and $7$ form a diagonal, so this tells you the total of each row, column and diagonal is $13+10+7=30$. The first column then has middle cell $30 - 13 - 9 = 8$, the bottom row has middle cell $30 - 9 - 7 = 14$ and the other diagonal has top-right cell $30 - 9 - 10 = 11$.

The other two cells can then be calculated in the same way, giving the completed grid as below:


This problem is taken from the UKMT Mathematical Challenges.
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