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.
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
Delight your friends with this cunning trick! Can you explain how
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.
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 explain how this card trick works?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Crosses can be drawn on number grids of various sizes. What do you
notice when you add opposite ends?
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?
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.
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?
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
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 your logical reasoning to work out how many cows and how many
sheep there are in each field.
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
What are the missing numbers in the pyramids?
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.
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
Can you be the first to complete a row of three?
This is an adding game for two players.
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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?
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. . . .
This article suggests some ways of making sense of calculations involving positive and negative numbers.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
This Sudoku, based on differences. Using the one clue number can you find the solution?
There are nasty versions of this dice game but we'll start with the nice ones...
If you have only four weights, where could you place them in order
to balance this equaliser?
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 score 100 by throwing rings on this board? Is there more
than way to do it?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.