### There are 12 results

Broad Topics >

Numbers and the Number System > Square numbers

##### Age 11 to 14 Challenge Level:

Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?

##### Age 14 to 16 Challenge Level:

Discover a way to sum square numbers by building cuboids from small
cubes. Can you picture how the sequence will grow?

##### Age 14 to 16 Challenge Level:

Robert noticed some interesting patterns when he highlighted square
numbers in a spreadsheet. Can you prove that the patterns will
continue?

##### Age 14 to 16 Challenge Level:

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?

##### Age 14 to 18 Challenge Level:

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

##### Age 14 to 18 Challenge Level:

Can you find some Pythagorean Triples where the two smaller numbers differ by 1?

##### Age 11 to 14 Challenge Level:

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?

##### Age 11 to 14 Challenge Level:

What is the value of the digit A in the sum below: [3(230 + A)]^2 =
49280A

##### Age 14 to 16 Challenge Level:

Which numbers can we write as a sum of square numbers?

##### Age 11 to 14 Challenge Level:

Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.

##### Age 11 to 14 Challenge Level:

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?

##### Age 11 to 14 Challenge Level:

Using your knowledge of the properties of numbers, can you fill all the squares on the board?