Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Can you explain how this card trick works?
Delight your friends with this cunning trick! Can you explain how it works?
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.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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?
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?
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 happens?
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?
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?
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?
This article suggests some ways of making sense of calculations involving positive and negative numbers.
Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.
Here is a chance to play a version of the classic Countdown Game.
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?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?
Replace each letter with a digit to make this addition correct.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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.
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!
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
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?
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?
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.
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?
On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?
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.
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 three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
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 jugs.
An environment which simulates working with Cuisenaire rods.
Can you score 100 by throwing rings on this board? Is there more than way to do it?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
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?