We have a challenge a day for you throughout the summer break...
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 Secondary Summer Challenges 2023.
Sealed Solution
Age 7 to 11
Challenge Level
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?
Fifteen Cards
Age 7 to 11
Challenge Level
Can you use the information to find out which cards I have used?
Roll These Dice
Age 7 to 11
Challenge Level
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?
Factor Track
Age 7 to 11
Challenge Level
Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.
Add 3 Dice
Age 7 to 11
Challenge Level
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 do this?
Biscuit Decorations
Age 5 to 7
Challenge Level
Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?
Teddy Town
Age 5 to 11
Challenge Level
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Sets of Numbers
Age 7 to 11
Challenge Level
How many different sets of numbers with at least four members can you find in the numbers in this box?
Square Corners
Age 7 to 11
Challenge Level
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
Skip Counting
Age 5 to 7
Challenge Level
Find the squares that Froggie skips onto to get to the pumpkin patch. She starts on 3 and finishes on 30, but she lands only on a square that has a number 3 more than the square she skips from.
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.
Seeing Squares
Age 5 to 11
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.
Family Tree
Age 7 to 11
Challenge Level
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
A City of Towers
Age 5 to 7
Challenge Level
In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
Seven Flipped
Age 7 to 11
Challenge Level
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
4 Dom
Age 5 to 11
Challenge Level
Use these four dominoes to make a square that has the same number of dots on each side.
Less Is More
Age 7 to 11
Challenge Level
Use your knowledge of place value to try to win this game. How will you maximise your score?
Robot Monsters
Age 5 to 7
Challenge Level
Use these head, body and leg pieces to make Robot Monsters which are different heights.
First Connect Three
Age 7 to 11
Challenge Level
Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?
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.
Junior Frogs
Age 5 to 11
Challenge Level
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Coded Hundred Square
Age 7 to 11
Challenge Level
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Make 37
Age 7 to 11
Challenge Level
Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick any ten numbers from the bags so that their total is 37?
Incey Wincey Spider
Age 5 to 7
Challenge Level
You'll need two dice to play this game against a partner. Will Incey Wincey make it to the top of the drain pipe or the bottom of the drain pipe first?
Nim-7
Age 5 to 11
Challenge Level
Can you work out how to win this game of Nim? Does it matter if you go first or second?
Tangrams
Age 5 to 11
Challenge Level
Can you make five differently sized squares from the interactive tangram pieces?
Four Triangles Puzzle
Age 5 to 11
Challenge Level
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
Making Sticks
Age 5 to 7
Challenge Level
Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?
Missing Middles
Age 5 to 7
Challenge Level
Can you work out the domino pieces which would go in the middle in each case to complete the pattern of these eight sets of three dominoes?
Factors and Multiples Game
Age 7 to 16
Challenge Level
A game in which players take it in turns to choose a number. Can you block your opponent?
Two-digit Targets
Age 5 to 7
Challenge Level
You have a set of the digits from 0 to 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?
Dicey Operations in Line
Age 7 to 11
Challenge Level
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
Shape Times Shape
Age 7 to 11
Challenge Level
These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?
Butterfly Flowers
Age 5 to 7
Challenge Level
Can you find two butterflies to go on each flower so that the numbers on each pair of butterflies adds to the number on their flower?
The Remainders Game
Age 7 to 14
Challenge Level
Play this game and see if you can figure out the computer's chosen number.
Sort the Street
Age 5 to 7
Challenge Level
Sort the houses in my street into different groups. Can you do it in any other ways?
Mystery Matrix
Age 7 to 11
Challenge Level
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
3 Blocks Towers
Age 5 to 7
Challenge Level
Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?
NRICH is part of the family of activities in the Millennium Mathematics Project.