We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?
Can you explain how this card trick works?
Delight your friends with this cunning trick! Can you explain how it works?
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Can you explain the strategy for winning this game with any target?
Find out about Magic Squares in this article written for students. Why are they magic?!
Here is a chance to play a version of the classic Countdown Game.
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
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 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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Can you find all the ways to get 15 at the top of this triangle of numbers?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
What are the missing numbers in the pyramids?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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?
This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.
In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.
Choose a symbol to put into the number sentence.
If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
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?
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!
If you have only four weights, where could you place them in order to balance this equaliser?
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Who said that adding couldn't be fun?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Replace each letter with a digit to make this addition correct.
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
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.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Find the sum of all three-digit numbers each of whose digits is odd.
How many solutions can you find to this sum? Each of the different letters stands for a different number.