Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

The clues for this Sudoku are the product of the numbers in adjacent squares.

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

A few extra challenges set by some young NRICH members.

You need to find the values of the stars before you can apply normal Sudoku rules.

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

How many different symmetrical shapes can you make by shading triangles or squares?

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

Use the differences to find the solution to this Sudoku.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

Find the values of the nine letters in the sum: FOOT + BALL = GAME

Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

A challenging activity focusing on finding all possible ways of stacking rods.

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?