Age 16 to 18 Challenge Level:
Why do this
It provides an opportunity for learners to experiment with
numerical examples, to observe a pattern and make a conjecture, to
try to explain their own conjecture and to formulate a proof of the
conjecture which involves only simple algebra.
Suggest that the learners make up their own examples similar to the
ones given and look for a pattern.
Can you see any relationship between the numbers in the
Is there any pattern in the relationship between the numbers?
If you spot a pattern can you prove it always occurs?
The problen page suggests an extension to three times the sum of
The pattern can be generalised to four times the sum of four
squares and so on (see the solution).
Suggest that learners find out which of the numbers from 1 to 10
can be written as the sum of 2 squares.
eg $1 = 1^2 + 0^2$