Square numbers

problem

A Square Deal

Age

7 to 11

Challenge level

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
problem

Picture a Pyramid

Age

7 to 11

Challenge level

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
problem

Seven Square Numbers

Age

7 to 11

Challenge level

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

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

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

Square Routes

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?
problem

Smith and Jones

Age

14 to 16

Challenge level

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

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

Triangles Within Squares

Age

14 to 16

Challenge level

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

Square Sum

Age

14 to 16

Challenge level

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