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 substitute numbers for the letters in these sums?
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?
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.
Follow the clues to find the mystery number.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
This 100 square jigsaw is written in code. It starts with 1 and
ends with 100. Can you build it up?
Can you find the chosen number from the grid using the clues?
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
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?
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
What two-digit numbers can you make with these two dice? What can't you make?
Have a go at balancing this equation. Can you find different ways of doing it?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Can you replace the letters with numbers? Is there only one
solution in each case?
What happens when you round these three-digit numbers to the nearest 100?
This activity focuses on rounding to the nearest 10.
Can you work out some different ways to balance this equation?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?
What happens when you round these numbers to the nearest whole number?
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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?
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?
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....?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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?
Find out what a "fault-free" rectangle is and try to make some of
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
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
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?
Can you find all the different ways of lining up these Cuisenaire
How many trains can you make which are the same length as Matt's,
using rods that are identical?
Alice's mum needs to go to each child's house just once and then
back home again. How many different routes are there? Use the
information to find out how long each road is on the route she
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
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?