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.

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

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

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

A few extra challenges set by some young NRICH members.

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

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's there is one digit, between the two 2's there are two digits, and between the two 3's there are three digits.

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?

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

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

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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 could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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

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

Use the differences to find the solution to this Sudoku.

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

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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 find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

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

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

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

Can you use the information to find out which cards I have used?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

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

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?

Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column

Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

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