A game for 2 players
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.
To avoid losing think of another very well known game where the patterns of play are similar.
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
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.
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.
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.
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.
The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
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 loser is the player who takes the last counter.
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
A collection of games on the NIM theme
Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible.
Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
Nim-7 game for an adult and child. Who will be the one 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.
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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?
A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you. . . .
Take any two positive numbers. Calculate the arithmetic and geometric means. Repeat the calculations to generate a sequence of arithmetic means and geometric means. Make a note of what happens to the. . . .
The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 × 1 [1/3]. What other numbers have the sum equal to the product and can this be so for. . . .
Can you describe this route to infinity? Where will the arrows take you next?
It starts quite simple but great opportunities for number discoveries and patterns!
Can you use the diagram to prove the AM-GM inequality?
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Can you find sets of sloping lines that enclose a square?
Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
It would be nice to have a strategy for disentangling any tangled ropes...
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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.
Can you tangle yourself up and reach any fraction?
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
How many moves does it take to swap over some red and blue frogs? Do you have a method?
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.
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.