This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
This challenge extends the Plants investigation so now four or more children are involved.
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
The letters of the word ABACUS have been arranged in the shape of a
triangle. How many different ways can you find to read the word
ABACUS from this triangular pattern?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Given the products of adjacent cells, can you complete this Sudoku?
You have been given nine weights, one of which is slightly heavier
than the rest. Can you work out which weight is heavier in just two
weighings of the balance?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Can you use the information to find out which cards I have used?
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
Find out what a "fault-free" rectangle is and try to make some of
A package contains a set of resources designed to develop
students’ mathematical thinking. This package places a
particular emphasis on “being systematic” and is
designed to meet. . . .
This package contains a collection of problems from the NRICH
website that could be suitable for students who have a good
understanding of Factors and Multiples and who feel ready to take
on some. . . .
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
How many different triangles can you make on a circular pegboard that has nine pegs?
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
Can you find all the different triangles on these peg boards, and
find their angles?
Can you find all the different ways of lining up these Cuisenaire
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
A few extra challenges set by some young NRICH members.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?