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.
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.
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.
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
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.
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.
The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
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.
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
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.
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
Find out what a "fault-free" rectangle is and try to make some of your own.
Here are two kinds of spirals for you to explore. What do you notice?
Think of a number, add one, double it, take away 3, add the number you first thought of, add 7, divide by 3 and take away the number you first thought of. You should now be left with 2. How do I. . . .
The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.
Can you explain how this card trick works?
Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
A collection of games on the NIM theme
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?
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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Can you find sets of sloping lines that enclose a square?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?
Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Delight your friends with this cunning trick! Can you explain how it works?
It starts quite simple but great opportunities for number discoveries and patterns!
You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .
This challenge asks you to imagine a snake coiling on itself.
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?
This activity involves rounding four-digit numbers to the nearest thousand.
What would be the smallest number of moves needed to move a Knight from a chess set from one corner to the opposite corner of a 99 by 99 square board?
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?
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
Can you explain the strategy for winning this game with any target?
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
It would be nice to have a strategy for disentangling any tangled ropes...
Can you find all the ways to get 15 at the top of this triangle of numbers?
Can you tangle yourself up and reach any fraction?
This task follows on from Build it Up and takes the ideas into three dimensions!
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Got It game for an adult and child. How can you play so that you know you will always win?