Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
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.
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
What are the missing numbers in the pyramids?
Replace each letter with a digit to make this addition correct.
Delight your friends with this cunning trick! Can you explain how
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?
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?
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
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.
Choose any three by three square of dates on a calendar page...
There are exactly 3 ways to add 4 odd numbers to get 10. Find all
the ways of adding 8 odd numbers to get 20. To be sure of getting
all the solutions you will need to be systematic. What about. . . .
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
This Sudoku, based on differences. Using the one clue number can you find the solution?
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Find the sum of all three-digit numbers each of whose digits is
Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.
Whenever two chameleons of different colours meet they change
colour to the third colour. Describe the shortest sequence of
meetings in which all the chameleons change to green if you start
with 12. . . .
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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.
Can you explain the strategy for winning this game with any target?
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 a great variety of ways of asking questions which make 8.
Complete these two jigsaws then put one on top of the other. What
happens when you add the 'touching' numbers? What happens when you
change the position of the jigsaws?
If each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the
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.
Are these statements always true, sometimes true or never true?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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.
Max and Mandy put their number lines together to make a graph. How
far had each of them moved along and up from 0 to get the counter
to the place marked?
Here is a chance to play a version of the classic Countdown Game.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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?
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?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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!
Number problems at primary level that require careful consideration.
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
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
In sheep talk the only letters used are B and A. A sequence of
words is formed by following certain rules. What do you notice when
you count the letters in each word?
You have 5 darts and your target score is 44. How many different
ways could you score 44?