Square numbers

problem
Augustus' age

Age

7 to 11

Challenge level

In 1871 a mathematician called Augustus De Morgan died. De Morgan made a puzzling statement about his age. Can you discover which year De Morgan was born in?
problem
Special 24

Age

7 to 11

Challenge level

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.
problem
A right Charlie

Age

7 to 11

Challenge level

Can you use this information to work out Charlie's house number?
problem
Iff

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?
problem
Triangular triples

Age

14 to 16

Challenge level

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

Age

11 to 14

Challenge level

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

Age

14 to 16

Challenge level

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.
problem
Time of birth

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?
problem
Little squares

Age

5 to 7

Challenge level

Look at the squares in this problem. What does the next square look like? I draw a square with 81 little squares inside it. How long and how wide is my square?