Toughnuts - Try These Unsolved Problems

All Change

Stage: 1 Challenge Level: Challenge Level:1

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

Sticky Data

Stage: 1 Challenge Level: Challenge Level:1

You'll need to work in a group on this problem. Can you use your sticky notes to show the answer to questions such as 'how many boys and girls are there in your group?'.

Poly Plug Pattern

Stage: 1 Challenge Level: Challenge Level:1

Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?

Taking Steps

Stage: 2 Challenge Level: Challenge Level:1

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

Machines

Stage: 2 Challenge Level: Challenge Level:1

What is happening at each box in these machines?

Birdwatch

Stage: 2 Challenge Level: Challenge Level:1

Have a look at this data from the RSPB 2011 Birdwatch. What can you say about the data?

Strike it Out

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

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

Attractive Tablecloths

Stage: 4 Challenge Level: Challenge Level:1

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?

Circle pdf

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

What happens if this pdf is the arc of a circle?

Uniformly Unstable

Stage: 5 Challenge Level: Challenge Level:1

Invent shapes with different numbers of stable and unstable equilibrium points

Phase Space

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Explore the issues surrounding the concept of Phase Space.

pdf Stories

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Invent scenarios which would give rise to these probability density functions.

Poison, Antidote, Water

Stage: 4 and 5 Challenge Level: Challenge Level:1

Play the game of Poison, Antidote, Water to start to understand the mathematics of associativity and groups.

Triathlon and Fitness

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?

LCM Sudoku

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

Speed-time Problems at the Olympics

Stage: 4 Challenge Level: Challenge Level:1

Have you ever wondered what it would be like to race against Usain Bolt?

Diverging

Stage: 5 Challenge Level: Challenge Level:1

Show that for natural numbers x and y if x/y > 1 then x/y>(x+1)/(y+1}>1. Hence prove that the product for i=1 to n of [(2i)/(2i-1)] tends to infinity as n tends to infinity.

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