This challenge extends the Plants investigation so now four or more children are involved.
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.
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
A challenging activity focusing on finding all possible ways of stacking rods.
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?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
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.
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
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?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
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?"
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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?
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
Can you find all the different ways of lining up these Cuisenaire
Can you find all the different triangles on these peg boards, and
find their angles?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
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....?
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. . . .
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. . . .
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 put the 25 coloured tiles into the 5 x 5 square so that no
column, no row and no diagonal line have tiles of the same colour
Find out what a "fault-free" rectangle is and try to make some of
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Can you use the information to find out which cards I have used?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
A few extra challenges set by some young NRICH members.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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?
In this matching game, you have to decide how long different events take.