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Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

##### Age 11 to 14 Challenge Level:

The following solution was sent to us by Josh (Alameda School)

The easiest way of seeing how it works is to use x as the first number.
Multiply by 3 makes it 3 x
Adding 6 makes it 3 x + 6
Taking away the start number makes it 2 x + 6
Then dividing by 2 makes it x + 3
Taking away the original number then leaves 3.

Well done Josh!

Wat Zhiwen Sergius (Anglo-Chines Primary School, Singapore) writes the solution this way... "Let n be the number (3n+6)-n = (2n+6) (2n+6)/2 = (n+3) (n+3)-3 = n