For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
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?
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.
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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?
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.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
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!
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
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
Here is a chance to play a version of the classic Countdown Game.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
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!
Got It game for an adult and child. How can you play so that you know you will always win?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit 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?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Are these statements always true, sometimes true or never true?
Can you find all the ways to get 15 at the top of this triangle of numbers?
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?
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.
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
I throw three dice and get 5, 3 and 2. Add the scores on the three
dice. What do you get? Now multiply the scores. What do you notice?
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.
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
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 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
Number problems at primary level that may require determination.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
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.
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
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.
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
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?