NRICH provides thousands of free online mathematics resources for ages 3 to 18, covering all stages of early years, primary and secondary school education – completely free and available to all.

One day our teacher asked us a puzzling question.

Play around with the Fibonacci sequence and discover some surprising results!

Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens…

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

The sum of five consecutive integers is equal to the sum of the next three consecutive integers. Can you find the largest of these integers?

How old will Julie be when her age is equal to the sum of her daughters’ ages?

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

These are the results when 3 numbers were added in pairs. What were the numbers?

Three numbers add up to 100. The difference between the larger two is 12 and the difference between the smaller two is 2. What are the numbers?

Amy misread a question and got an incorrect answer. What should the answer have be?

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

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

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.

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

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

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?

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

 How much money did the pensioner have before being robbed?