Find the sum of all three-digit numbers each of whose digits is
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
Got It game for an adult and child. How can you play so that you know you will always win?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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.
This activity involves rounding four-digit numbers to the nearest thousand.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
This article for teachers describes several games, found on the
site, all of which have a related structure that can be used to
develop the skills of strategic planning.
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
While we were sorting some papers we found 3 strange sheets which
seemed to come from small books but there were page numbers at the
foot of each page. Did the pages come from the same book?
Find out what a "fault-free" rectangle is and try to make some of
A game for 2 players with similaritlies to NIM. Place one counter on each spot on the games board. Players take it is turns to remove 1 or 2 adjacent counters. The winner picks up the last counter.
Can you explain how this card trick works?
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
What happens when you round these numbers to the nearest whole number?
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?
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
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.
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.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
A collection of games on the NIM theme
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
A game for 2 players. Set out 16 counters in rows of 1,3,5 and 7. Players take turns to remove any number of counters from a row. The player left with the last counter looses.
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
This challenge asks you to imagine a snake coiling on itself.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
What happens when you round these three-digit numbers to the nearest 100?
Delight your friends with this cunning trick! Can you explain how
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Can you find all the ways to get 15 at the top of this triangle of numbers?
This task follows on from Build it Up and takes the ideas into three dimensions!
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Are these statements relating to odd and even numbers always true, sometimes true or never true?
One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
Can you dissect an equilateral triangle into 6 smaller ones? What
number of smaller equilateral triangles is it NOT possible to
dissect a larger equilateral triangle into?
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.
Are these statements always true, sometimes true or never true?
Here are two kinds of spirals for you to explore. What do you notice?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?