Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

In this matching game, you have to decide how long different events take.

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

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

My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

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

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

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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?

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?

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

The pages of my calendar have got mixed up. Can you sort them out?

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?

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

Try out the lottery that is played in a far-away land. What is the chance of winning?

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

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?

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

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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

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

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?

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?

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

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

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?

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

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

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

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

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?

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....?

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

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?

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.

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

A few extra challenges set by some young NRICH members.

How many different triangles can you make on a circular pegboard that has nine pegs?

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

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?