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?
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.
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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.
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Find out what a "fault-free" rectangle is and try to make some of your own.
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
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?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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 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.
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?
A Sudoku with clues as ratios.
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
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?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?
Given the products of adjacent cells, can you complete this Sudoku?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
A Sudoku that uses transformations as supporting clues.
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?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Can you find all the different triangles on these peg boards, and find their angles?
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?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
A few extra challenges set by some young NRICH members.
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?
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.
In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?