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 Primary Interactive Summer Challenges 2022.
What Numbers Can We Make Now?
Age 11 to 14
Challenge Level
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
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?
The Remainders Game
Age 7 to 14
Challenge Level
Play this game and see if you can figure out the computer's chosen number.
Polygon Rings
Age 11 to 14
Challenge Level
Join pentagons together edge to edge. Will they form a ring?
L-triominoes
Age 14 to 16
Challenge Level
L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?
Latin Lilies
Age 7 to 14
Challenge Level
In this game you are challenged to gain more columns of lily pads than your opponent.
Diamond Collector
Age 11 to 16
Challenge Level
Collect as many diamonds as you can by drawing three straight lines.
Stars
Age 11 to 14
Challenge Level
Can you work out what step size to take to ensure you visit all the dots on the circle?
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?
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?
In the Bag
Age 11 to 14
Challenge Level
Can you guess the colours of the 10 marbles in the bag? Can you develop an effective strategy for reaching 1000 points in the least number of rounds?
Tilted Squares
Age 11 to 14
Challenge Level
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Semi-regular Tessellations
Age 11 to 16
Challenge Level
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Countdown
Age 7 to 14
Challenge Level
Here is a chance to play a version of the classic Countdown Game.
The Better Choice
Age 14 to 16
Challenge Level
Here are two games you can play. Which offers the better chance of winning?
Last Biscuit
Age 11 to 18
Challenge Level
Can you find a strategy that ensures you get to take the last biscuit in this game?
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?
Comparing Carbon Footprints
Age 11 to 18
Challenge Level
This interactivity is designed to help you gain a better understanding of how your lifestyle choices can affect your carbon footprint.
Magic Potting Sheds
Age 11 to 16
Challenge Level
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
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?
3D Treasure Hunt
Age 14 to 18
Challenge Level
Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?
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?
Beelines
Age 14 to 16
Challenge Level
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
Nine Colours
Age 11 to 16
Challenge Level
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
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?
Square Coordinates
Age 11 to 14
Challenge Level
A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?
Charlie's Delightful Machine
Age 11 to 16
Challenge Level
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Isosceles Triangles
Age 11 to 14
Challenge Level
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
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.
Finding Factors
Age 14 to 16
Challenge Level
Can you find the hidden factors which multiply together to produce each quadratic expression?
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?
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?
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?
The Number Jumbler
Age 7 to 14
Challenge Level
The Number Jumbler can always work out your chosen symbol. Can you work out how?
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.
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?
NRICH is part of the family of activities in the Millennium Mathematics Project.