We have a challenge a day for you throughout the summer break...
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Each weekday, from 10 July to 1 September, a new problem or game will appear on this page.
After you've had a go at the day's challenge you may be able to compare your approach to the solutions we have published, which are based on students' work.
You can also find Primary Summer Challenges 2023.
problem
What's Possible?
Age
14 to 16
Challenge level
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
problem
Why 24?
Age
14 to 16
Challenge level
Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.
problem
Where can we visit?
Age
11 to 14
Challenge level
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
problem
American Billions
Age
11 to 14
Challenge level
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
problem
Frogs
Age
11 to 14
Challenge level
How many moves does it take to swap over some red and blue frogs? Do you have a method?
problem
Cinema Problem
Age
11 to 14
Challenge level
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
problem
Take Three From Five
Age
11 to 16
Challenge level
Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?
problem
Special Numbers
Age
11 to 14
Challenge level
My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
problem
Pair Products
Age
14 to 16
Challenge level
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
problem
Peaches today, Peaches tomorrow...
Age
11 to 14
Challenge level
A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?
problem
Tourism
Age
11 to 14
Challenge level
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.
problem
Square It
Age
11 to 16
Challenge level
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
problem
Consecutive Seven
Age
11 to 14
Challenge level
Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?
problem
Product Sudoku
Age
11 to 16
Challenge level
The clues for this Sudoku are the product of the numbers in adjacent squares.
problem
Substitution Cipher
Age
11 to 14
Challenge level
Find the frequency distribution for ordinary English, and use it to help you crack the code.
problem
Factors and Multiples Puzzle
Age
11 to 14
Challenge level
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
problem
Route to infinity
Age
11 to 14
Challenge level
Can you describe this route to infinity? Where will the arrows take you next?
problem
Connect Three
Age
11 to 16
Challenge level
In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?
problem
crossing the bridge
Age
11 to 18
Challenge level
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
problem
Zin Obelisk
Age
11 to 14
Challenge level
In the ancient city of Atlantis a solid rectangular object called a Zin was built in honour of the goddess Tina. Your task is to determine on which day of the week the obelisk was completed.
problem
Multiples Sudoku
Age
11 to 14
Challenge level
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
problem
Sticky Numbers
Age
11 to 14
Challenge level
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
problem
Always a multiple?
Age
11 to 14
Challenge level
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
problem
Sociable Cards
Age
11 to 14
Challenge level
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
problem
What numbers can we make?
Age
11 to 14
Challenge level
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
problem
Magic Letters
Age
11 to 14
Challenge level
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
problem
Kite in a Square
Age
14 to 18
Challenge level
Can you make sense of the three methods to work out what fraction of the total area is shaded?
problem
Olympic Measures
Age
11 to 14
Challenge level
These Olympic quantities have been jumbled up! Can you put them back together again?
problem
Add to 200
Age
11 to 14
Challenge level
By selecting digits for an addition grid, what targets can you make?
problem
Forwards Add Backwards
Age
11 to 14
Challenge level
What happens when you add a three digit number to its reverse?
problem
Overlaps
Age
11 to 14
Challenge level
Can you find ways to put numbers in the overlaps so the rings have equal totals?
problem
Gabriel's Problem
Age
11 to 14
Challenge level
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
problem
More Less is More
Age
7 to 14
Challenge level
In each of these games, you will need a little bit of luck, and your knowledge of place value to develop a winning strategy.
problem
Dozens
Age
7 to 14
Challenge level
Can you select the missing digit(s) to find the largest multiple?
problem
Got It
Age
7 to 14
Challenge level
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.