There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
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.
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
When I type a sequence of letters my calculator gives the product
of all the numbers in the corresponding memories. What numbers
should I store so that when I type 'ONE' it returns 1, and when I
type. . . .
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?
What is the largest number you can make using the three digits 2, 3
and 4 in any way you like, using any operations you like? You can
only use each digit once.
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
What is the sum of all the digits in all the integers from one to
There are nasty versions of this dice game but we'll start with the nice ones...
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
This article suggests some ways of making sense of calculations involving positive and negative numbers.
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
An environment which simulates working with Cuisenaire rods.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
Can you substitute numbers for the letters in these sums?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
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?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
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?
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.
This dice train has been made using specific rules. How many different trains can you make?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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
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.
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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!
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?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
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?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
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?
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
If you have only four weights, where could you place them in order
to balance this equaliser?
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.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!