It would be nice to have a strategy for disentangling any tangled
Can you tangle yourself up and reach any fraction?
The Egyptians expressed all fractions as the sum of different unit
fractions. Here is a chance to explore how they could have written
This challenge asks you to imagine a snake coiling on itself.
Can all unit fractions be written as the sum of two unit fractions?
The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 × 1 [1/3]. What other numbers have the sum equal to the product and can this be so for. . . .
Can you see how to build a harmonic triangle? Can you work out the next two rows?
Find some examples of pairs of numbers such that their sum is a
factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and
16 is a factor of 48.
Charlie has moved between countries and the average income of both
has increased. How can this be so?
Can you describe this route to infinity? Where will the arrows take you next?
What would you get if you continued this sequence of fraction sums?
1/2 + 2/1 =
2/3 + 3/2 =
3/4 + 4/3 =
Problem solving is at the heart of the NRICH site. All the problems
give learners opportunities to learn, develop or use mathematical
concepts and skills. Read here for more information.
The aim of the game is to slide the green square from the top right
hand corner to the bottom left hand corner in the least number of
Pick a square within a multiplication square and add the numbers on
each diagonal. What do you notice?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Imagine starting with one yellow cube and covering it all over with
a single layer of red cubes, and then covering that cube with a
layer of blue cubes. How many red and blue cubes would you need?
We can show that (x + 1)² = x² + 2x + 1 by considering
the area of an (x + 1) by (x + 1) square. Show in a similar way
that (x + 2)² = x² + 4x + 4
An investigation that gives you the opportunity to make and justify
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
A package contains a set of resources designed to develop
pupils’ mathematical thinking. This package places a
particular emphasis on “generalising” and is designed
to meet the. . . .
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Find out what a "fault-free" rectangle is and try to make some of
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.
A collection of games on the NIM theme
Jo has three numbers which she adds together in pairs. When she
does this she has three different totals: 11, 17 and 22 What are
the three numbers Jo had to start with?”
Start with any number of counters in any number of piles. 2 players
take it in turns to remove any number of counters from a single
pile. The winner is the player to take the last counter.
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?
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
Can you find the values at the vertices when you know the values on
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
In this problem we are looking at sets of parallel sticks that
cross each other. What is the least number of crossings you can
make? And the greatest?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
This activity involves rounding four-digit numbers to the nearest thousand.
What happens when you round these numbers to the nearest whole number?
What happens when you round these three-digit numbers to the nearest 100?
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
It starts quite simple but great opportunities for number discoveries and patterns!
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.