Challenge Level

A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

Challenge Level

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

Challenge Level

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

Challenge Level

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

Challenge Level

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

Challenge Level

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

Challenge Level

The sums of the squares of three related numbers is also a perfect square - can you explain why?

Challenge Level

Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?

Challenge Level

Can you find the hidden factors which multiply together to produce each quadratic expression?

Challenge Level

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

Challenge Level

If you know the perimeter of a right angled triangle, what can you say about the area?

Challenge Level

What is special about the difference between squares of numbers adjacent to multiples of three?

Challenge Level

Which armies can be arranged in hollow square fighting formations?

Challenge Level

Can you see how to build a harmonic triangle? Can you work out the next two rows?

A collection of short problems on creating algebraic expressions.

Challenge Level

There are unexpected discoveries to be made about square numbers...

Challenge Level

Can you explain what is going on in these puzzling number tricks?

Challenge Level

Brian chooses an integer and operates on it. Work out the largest integer that he could have chosen.

Challenge Level

Can you work out how many members this choir has from these percentages?

Challenge Level

Can you find the volume of a cuboid, given its perimeters?

Challenge Level

What are the possible lengths for the third side of this right-angled triangle?

Challenge Level

How much money did the pensioner have before being robbed?

Challenge Level

Find the shortcut to do this calculation quickly!

Challenge Level

The area of a rectangle is 225 square units. Find its width.