Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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.
Can you explain how this card trick works?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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.
Delight your friends with this cunning trick! Can you explain how
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?
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
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 find six numbers to go in the Daisy from which you can make
all the numbers from 1 to a number bigger than 25?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
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?
This article suggests some ways of making sense of calculations involving positive and negative numbers.
Replace each letter with a digit to make this addition correct.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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.
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
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
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?
Here is a chance to play a version of the classic Countdown Game.
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. . . .
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 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?
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
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 put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
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.
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
This challenge extends the Plants investigation so now four or more children are involved.
Can you be the first to complete a row of three?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
There are nasty versions of this dice game but we'll start with the nice ones...
This Sudoku, based on differences. Using the one clue number can you find the solution?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
If you have only four weights, where could you place them in order
to balance this equaliser?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
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?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Choose a symbol to put into the number sentence.
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?