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. . . .

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

This Sudoku requires you to do some working backwards before working forwards.

How many different rectangles can you make using this set of rods?

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?

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

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?

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

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?

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 ...?

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?

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

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

Given the products of diagonally opposite cells - can you complete this Sudoku?

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

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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

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.

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.

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?

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.

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

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

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

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

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

A few extra challenges set by some young NRICH members.

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

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

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?

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

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

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

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

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?

Find out about Magic Squares in this article written for students. Why are they magic?!

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....?