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.
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.
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.
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 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 explain the strategy for winning this game with any target?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
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?
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
Can you find the values at the vertices when you know the values on the edges?
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
Got It game for an adult and child. How can you play so that you know you will always win?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
A game for 2 players
A collection of games on the NIM theme
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
To avoid losing think of another very well known game where the patterns of play are similar.
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.
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.
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.
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!
Can all unit fractions be written as the sum of two unit fractions?
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. . . .
The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.
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.
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
Dave Hewitt suggests that there might be more to mathematics than looking at numerical results, finding patterns and generalising.
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.
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
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.
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.
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
Make some loops out of regular hexagons. What rules can you discover?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
It would be nice to have a strategy for disentangling any tangled ropes...
Can you use the diagram to prove the AM-GM inequality?
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. . . .
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?
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
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. . . .
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?
Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .
These gnomons appear to have more than a passing connection with the Fibonacci sequence. This problem ask you to investigate some of these connections.
Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?