Square numbers

problem

Seven Square Numbers

Age

7 to 11

Challenge level

3 out of 3

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.
problem

Four Coloured Lights

Age

11 to 14

Challenge level

2 out of 3

Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up?
problem

Square Triangle

Age

11 to 14

Challenge level

2 out of 3

How many triangles have all three angles perfect squares (in degrees)?
problem

Square Routes

Age

11 to 14

Challenge level

3 out of 3

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?
problem

Smith and Jones

Age

14 to 16

Challenge level

1 out of 3

Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!
problem

Pythagorean Quadruple

Age

14 to 16

Challenge level

1 out of 3

The sum of three square numbers equals $121$. What can those numbers be...
problem

Triangles Within Squares

Age

14 to 16

Challenge level

2 out of 3

Can you find a rule which relates triangular numbers to square numbers?
problem

Square Sum

Age

14 to 16

Challenge level

2 out of 3

One of these numbers is the largest of nine consecutive positive integers whose sum is a perfect square. Which one is it?
problem

Summing Squares

Age

14 to 16

Challenge level

2 out of 3

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

Robert's Spreadsheet

Age

14 to 16

Challenge level

2 out of 3

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