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

Use the clues about the symmetrical properties of these letters to place them on the grid.

This challenge extends the Plants investigation so now four or more children are involved.

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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?

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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.

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

This Sudoku, based on differences. Using the one clue number can you find the solution?

What is the best way to shunt these carriages so that each train can continue its journey?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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.

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

How long does it take to brush your teeth? Can you find the matching length of time?

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?

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?

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Two sudokus in one. Challenge yourself to make the necessary connections.

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

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?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

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.

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

Four small numbers give the clue to the contents of the four surrounding cells.

Can you find all the different triangles on these peg boards, and find their angles?

Two sudokus in one. Challenge yourself to make the necessary connections.

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?