Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was. . . .
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?
This is an adding game for two players.
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 challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
This challenge extends the Plants investigation so now four or more children are involved.
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?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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. . . .
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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 Sudoku, based on differences. Using the one clue number can you find the solution?
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 explain how this card trick works?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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.
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.
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?
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
Have a go at this game which involves throwing two dice and adding
their totals. Where should you place your counters to be more
likely to win?
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!
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Replace each letter with a digit to make this addition correct.
If you have only four weights, where could you place them in order
to balance this equaliser?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
If you wrote all the possible four digit numbers made by using each
of the digits 2, 4, 5, 7 once, what would they add up to?
Here is a chance to play a version of the classic Countdown Game.
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
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?
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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
Ben has five coins in his pocket. How much money might he have?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.