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Always the Same

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?

Mind Reader

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