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#### Resources tagged with Generalising similar to Tantrix Discovery:

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### Nim-7 for Two

##### Stage: 1 and 2 Challenge Level:

Nim-7 game for an adult and child. Who will be the one to take the last counter?

### Nim-7

##### Stage: 1, 2 and 3 Challenge Level:

Can you work out how to win this game of Nim? Does it matter if you go first or second?

### Domino Numbers

##### Stage: 2 Challenge Level:

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

### Number Differences

##### Stage: 2 Challenge Level:

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?

### Play to 37

##### Stage: 2 Challenge Level:

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.

### Roll over the Dice

##### Stage: 2 Challenge Level:

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?

### Dice Stairs

##### Stage: 2 Challenge Level:

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

### Walking the Squares

##### Stage: 2 Challenge Level:

Find a route from the outside to the inside of this square, stepping on as many tiles as possible.

### Dotty Circle

##### Stage: 2 Challenge Level:

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

### Fault-free Rectangles

##### Stage: 2 Challenge Level:

Find out what a "fault-free" rectangle is and try to make some of your own.

### The Add and Take-away Path

##### Stage: 1 Challenge Level:

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

### More Numbers in the Ring

##### Stage: 1 Challenge Level:

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

### Button-up Some More

##### Stage: 2 Challenge Level:

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

### Polygonals

##### Stage: 2 Challenge Level:

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

### Area and Perimeter

##### Stage: 2 Challenge Level:

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

### Strike it Out

##### Stage: 1 and 2 Challenge Level:

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

### Triangle Pin-down

##### Stage: 2 Challenge Level:

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

### Centred Squares

##### Stage: 2 Challenge Level:

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

### Spirals, Spirals

##### Stage: 2 Challenge Level:

Here are two kinds of spirals for you to explore. What do you notice?

### Broken Toaster

##### Stage: 2 Short Challenge Level:

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

### Snake Coils

##### Stage: 2 Challenge Level:

This challenge asks you to imagine a snake coiling on itself.

### Round the Four Dice

##### Stage: 2 Challenge Level:

This activity involves rounding four-digit numbers to the nearest thousand.

### Strike it Out for Two

##### Stage: 1 and 2 Challenge Level:

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

### Stop the Clock for Two

##### Stage: 1 Challenge Level:

Stop the Clock game for an adult and child. How can you make sure you always win this game?

### Build it up More

##### Stage: 2 Challenge Level:

This task follows on from Build it Up and takes the ideas into three dimensions!

### Build it Up

##### Stage: 2 Challenge Level:

Can you find all the ways to get 15 at the top of this triangle of numbers?

### Simple Train Journeys

##### Stage: 1 and 2 Challenge Level:

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

### Got it for Two

##### Stage: 2 Challenge Level:

Got It game for an adult and child. How can you play so that you know you will always win?

### Round the Three Dice

##### Stage: 2 Challenge Level:

What happens when you round these three-digit numbers to the nearest 100?

### Unit Differences

##### Stage: 1 Challenge Level:

This challenge is about finding the difference between numbers which have the same tens digit.

### Sums and Differences 1

##### Stage: 2 Challenge Level:

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

### Sums and Differences 2

##### Stage: 2 Challenge Level:

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?

### Crossings

##### Stage: 2 Challenge Level:

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?

### Sliding Puzzle

##### Stage: 1, 2, 3 and 4 Challenge Level:

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.

### Pentanim

##### Stage: 2, 3 and 4 Challenge Level:

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.

### Growing Garlic

##### Stage: 1 Challenge Level:

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

### Stop the Clock

##### Stage: 1 Challenge Level:

This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

### Games Related to Nim

##### Stage: 1, 2, 3 and 4

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.

### Calendar Calculations

##### Stage: 2 Challenge Level:

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

### Maths Trails

##### Stage: 2 and 3

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.

### Magic Circles

##### Stage: 2 Challenge Level:

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?

### Oddly

##### Stage: 2 Challenge Level:

Find the sum of all three-digit numbers each of whose digits is odd.

### Cut it Out

##### Stage: 2 Challenge Level:

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?

### Winning Lines

##### Stage: 2, 3 and 4

An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.

### Taking Steps

##### Stage: 2 Challenge Level:

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

### Lots of Lollies

##### Stage: 1 Challenge Level:

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

### Tiling

##### Stage: 2 Challenge Level:

An investigation that gives you the opportunity to make and justify predictions.

### Cuisenaire Rods

##### Stage: 2 Challenge Level:

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

### What Could it Be?

##### Stage: 1 Challenge Level:

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

### Round the Two Dice

##### Stage: 1 Challenge Level:

This activity focuses on rounding to the nearest 10.