In this article, the NRICH team describe the process of selecting solutions for publication on the site.
This article for primary teachers suggests ways in which to help children become better at working systematically.
Can you work out some different ways to balance this equation?
This activity focuses on rounding to the nearest 10.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
What two-digit numbers can you make with these two dice? What can't you make?
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
What happens when you round these three-digit numbers to the nearest 100?
What happens when you round these numbers to the nearest whole number?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Have a go at balancing this equation. Can you find different ways of doing it?
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.
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
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?
If you put three beads onto a tens/ones abacus you could make the
numbers 3, 30, 12 or 21. What numbers can be made with six beads?
Follow the clues to find the mystery number.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Can you find the chosen number from the grid using the clues?
This challenge extends the Plants investigation so now four or more children are involved.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Can you replace the letters with numbers? Is there only one
solution in each case?
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 100 square jigsaw is written in code. It starts with 1 and
ends with 100. Can you build it up?
In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
Can you substitute numbers for the letters in these sums?
Find out about Magic Squares in this article written for students. Why are they magic?!
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....?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
An investigation that gives you the opportunity to make and justify
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Can you find all the different ways of lining up these Cuisenaire
Find out what a "fault-free" rectangle is and try to make some of
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
Can you make a train the same length as Laura's but using three
differently coloured rods? Is there only one way of doing it?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?