We have a challenge a day for you throughout the summer break...
Each weekday, from 18 July to 2 September, a new interactive game or puzzle 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 Interactive Summer Challenges 2022.
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.
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.
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?
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?
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?
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?
Growing Garlic
Age 5 to 11
Challenge Level
Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?
Remainders
Age 7 to 14
Challenge Level
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
Latin Lilies
Age 7 to 14
Challenge Level
In this game you are challenged to gain more columns of lily pads than your opponent.
Gathering Gems
Age 5 to 11
Challenge Level
Using compass points, can you describe up to ten paths on this map so that you bring as many gems back home as possible?
Largest Even
Age 5 to 7
Challenge Level
How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?
Carroll Diagrams
Age 5 to 11
Challenge Level
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Phiddlywinks
Age 7 to 18
Challenge Level
Have a go at this version of John Conway's game. Do you have any good strategies for winning?
Number Balance
Age 5 to 7
Challenge Level
Can you hang weights in the right place to make the the number balance balanced?
Tangram Browser
Age 7 to 11
Explore our selection of interactive tangrams. Can you use the tangram pieces to re-create each picture?
Seesaw Shenanigans
Age 3 to 7
Challenge Level
A group of animals has made a seesaw in the woods. How can you make the seesaw balance?
Countdown
Age 7 to 14
Challenge Level
Here is a chance to play a version of the classic Countdown Game.
Matching Fractions
Age 7 to 11
Challenge Level
Can you find different ways of showing the same fraction? Try this matching game and see.
Matching Numbers
Age 5 to 7
Challenge Level
Can you find different ways of showing the same number? Try this matching game and see!
Same Length Trains
Age 5 to 7
Challenge Level
How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?
Train Tactics
Age 7 to 11
Challenge Level
A train building game for two players. Can you be the one to complete the train?
Number Lines in Disguise
Age 7 to 14
Challenge Level
Some of the numbers have fallen off Becky's number line. Can you figure out what they were?
Sizing Them Up
Age 5 to 7
Challenge Level
Can you put these shapes in order of size? Start with the smallest.
Treasure Hunt
Age 7 to 14
Challenge Level
Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
Poly Plug Rectangles
Age 5 to 11
Challenge Level
The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?
Ducking and Dividing
Age 7 to 11
Challenge Level
Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?
Your Number Is...
Age 7 to 14
Challenge Level
Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?
Light the Lights
Age 5 to 7
Challenge Level
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
Tables Teaser
Age 5 to 7
Challenge Level
How will you work out which numbers have been used to create this multiplication square?
Fruity Totals
Age 7 to 16
Challenge Level
In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?
The Number Jumbler
Age 7 to 14
Challenge Level
The Number Jumbler can always work out your chosen symbol. Can you work out how?
NRICH is part of the family of activities in the Millennium Mathematics Project.