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