Robert noticed some interesting patterns when he highlighted square
numbers in a spreadsheet. Can you prove that the patterns will
Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?
Prove that if n is a triangular number then 8n+1 is a square number. Prove, conversely, that if 8n+1 is a square number then n is a triangular number.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
How many four digit square numbers are composed of even numerals?
What four digit square numbers can be reversed and become the
square of another number?
A square patio was tiled with square tiles all the same size. Some
of the tiles were removed from the middle of the patio in order to
make a square flower bed, but the number of the remaining tiles. . . .
Which numbers can we write as a sum of square numbers?
A woman was born in a year that was a square number, lived a square
number of years and died in a year that was also a square number.
When was she born?
Discover a way to sum square numbers by building cuboids from small
cubes. Can you picture how the sequence will grow?
What is the value of the digit A in the sum below: [3(230 + A)]^2 =
Using your knowledge of the properties of numbers, can you fill all the squares on the board?