Nim-7 game for an adult and child. Who will be the one to take the last counter?
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.
Got It game for an adult and child. How can you play so that you know you will always win?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Can you work out how to win this game of Nim? Does it matter if you go first or second?
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.
The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Find the sum of all three-digit numbers each of whose digits is odd.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
Find out what a "fault-free" rectangle is and try to make some of your own.
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.
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.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
This challenge asks you to imagine a snake coiling on itself.
This activity involves rounding four-digit numbers to the nearest thousand.
Can you explain how this card trick works?
Here are two kinds of spirals for you to explore. What do you notice?
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?
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?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
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?
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?
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.
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
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.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
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.
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.
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?
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?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
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?
Are these statements always true, sometimes true or never true?
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!
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?