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.
Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
A game for 2 players
To avoid losing think of another very well known game where the patterns of play are similar.
Can you find the values at the vertices when you know the values on the edges?
A game for 2 players with similarities 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 the strategy for winning this game with any target?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Delight your friends with this cunning trick! Can you explain how it works?
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?
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?
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Can you explain how this card trick works?
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
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.
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
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?
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?
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.
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.
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
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.
Can you work out how to win this game of Nim? Does it matter if you go first or second?
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Got It game for an adult and child. How can you play so that you know you will always win?
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?
Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?
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 starts quite simple but great opportunities for number discoveries and patterns!
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.
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
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.
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 moves does it take to swap over some red and blue frogs? Do you have a method?
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
What's the largest volume of box you can make from a square of paper?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”
Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel. . . .
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. . . .
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.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?