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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.

Here is an example:

3 by 3 square, with numbers 5 (circled), 6 (crossed out), 7 (crossed out) on the top line, 12, 13, and 14 on the middle line, and 19, 20 and 21 on the bottom line.

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?

Will the result be the same if you choose different numbers to circle?

Do you think the results would be different if you used a four by four square and end up with four circled numbers? Why?

Use your calendar to find a four by four square to test your hypothesis.

Choose another three by three square of numbers from the calendar page.

Add the numbers in the four corners.

Add the numbers in each row, then each column and diagonal that passes through the centre number. Can you discover why you get the results that you do?

Find the total for all of the numbers that are in the right and the left columns. Can you explain this answer?

What do you think will happen if you choose another set of nine numbers? Try it and see if your prediction is correct.

Choose other sized squares of numbers to try these investigations with.

Predict what the results might be.

What previous information will help you predict the results?

What would happen if you chose a rectangle on the calendar rather than a square?