These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
Find another number that is one short of a square number and when
you double it and add 1, the result is also a square number.
The following solution was offered by Trevor
of Riccarton High School, Christchruch, New Zealand. Other correct
solutions were received from Andrei (School 205, Bucharest), Mary
(Birchwood Community High School), Rachel and Sebastian (Hethersett
High School) and Claire.
...then I searched for pairs of square numbers that when one is
reversed, it will be the same as the second, but not including
pairs: $144$, $4414
...then the final clue is that Charle's car registration number
is a four digit number which is also a square number
as well, and is formed by repeating the last digit of the house
number, and using the numbers which I have picked...
...I can pick a square number from here, if there is
one......$1444$ is a square of $38$! So that means that $144$ is