Delight your friends with this cunning trick! Can you explain how
Can you explain how this card trick works?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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.
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.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number.
Cross out the numbers on the same row and column. Repeat this
process. Add up you four numbers. Why do they always add up to 34?
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?
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
Crosses can be drawn on number grids of various sizes. What do you
notice when you add opposite ends?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
This article suggests some ways of making sense of calculations involving positive and negative numbers.
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
This is an adding game for two players.
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.
Here is a chance to play a version of the classic Countdown Game.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
What are the missing numbers in the pyramids?
Choose any three by three square of dates on a calendar page.
Circle any number on the top row, put a line through the other
numbers that are in the same row and column as your circled number.
Repeat. . . .
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
Three dice are placed in a row. Find a way to turn each one so that
the three numbers on top of the dice total the same as the three
numbers on the front of the dice. Can you find all the ways to. . . .
Replace each letter with a digit to make this addition correct.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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?
Find the sum of all three-digit numbers each of whose digits is
There are nasty versions of this dice game but we'll start with the nice ones...
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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.
This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.
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?
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
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?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
In this game, you can add, subtract, multiply or divide the numbers
on the dice. Which will you do so that you get to the end of the
number line first?
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Choose a symbol to put into the number sentence.
Can you be the first to complete a row of three?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.