Toughnuts

 

Try these unsolved problems

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Clock Face

Stage:2 Challenge Level:Challenge Level:1

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

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Putting Two and Two Together

Stage:2 Challenge Level:Challenge Level:1

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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Locate the Lion's Lair

Stage:2 Challenge Level:Challenge Level:1

Use the sightings of the lion to guess the location of its lair.

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How Random!

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

Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?

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Largest Product

Stage:3 Challenge Level:Challenge Level:1

Which set of numbers that add to 10 have the largest product?

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In the Bag

Stage:3 Challenge Level:Challenge Level:1

Can you guess the colours of the 10 marbles in the bag? Can you develop an effective strategy for reaching 1000 points in the least number of rounds?

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Reaction Timer

Stage:3 Challenge Level:Challenge Level:1

What are your reactions like and what affects them?

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Playing Connect Three

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

In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?

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Conway's Chequerboard Army

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

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

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Which Spinners?

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

Which spinners were used to generate these frequency charts?

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Where Is the Dot?

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

A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?

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First Connect Three

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

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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A Scale for the Solar System

Stage:4 Challenge Level:Challenge Level:1

The Earth is further from the Sun than Venus, but how much further? Twice as far? Ten times?

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The Perforated Cube

Stage:4 Challenge Level:Challenge Level:1

A cube is made from smaller cubes, 5 by 5 by 5, then some of those cubes are removed. Can you make the specified shapes, and what is the most and least number of cubes required ?

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The Invertible Trefoil

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

When is a knot invertible ?

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Distribution Differences

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

How could you compare different situation where something random happens ? What sort of things might be the same ? What might be different ?

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Tri-split

Stage:4 Challenge Level:Challenge Level:3Challenge Level:3Challenge Level:3

A point P is selected anywhere inside an equilateral triangle. What can you say about the sum of the perpendicular distances from P to the sides of the triangle? Can you prove your conjecture?

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Modular Knights

Stage:5 Challenge Level:Challenge Level:1

Try to move the knight to visit each square once and return to the starting point. Move either 2 steps one way and one perpendicular (as in chess) or generalise to a steps one way and b the other.

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More Bridge Building

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

Which parts of these framework bridges are in tension and which parts are in compression?

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Road Maker 2

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

Can you work out where the blue-and-red brick roads end?

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Scale Invariance

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

By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.

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Spot the Difference

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

If you plot these graphs they may look the same, but are they?

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Circular Circuitry

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

What will happen when you switch on these circular circuits?

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Random Inequalities

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

Can you build a distribution with the maximum theoretical spread?

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Harmonically

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

Is it true that a large integer m can be taken such that: 1 + 1/2 + 1/3 + ... +1/m > 100 ?

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Pattern Recognition

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

When does a pattern start to exhibit structure? Can you crack the code used by the computer?

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Giant Holly Leaf

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

Find the perimeter and area of a holly leaf that will not lie flat (it has negative curvature with 'circles' having circumference greater than 2πr).

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Impossible Triangles?

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

Which of these triangular jigsaws are impossible to finish?

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Lion Hunting

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

A killer lion is causing devastation. From the locations of its reported activity, can you work out where its lair is located?

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Pentagon from 1926

Stage:4 and 5 Challenge Level:Challenge Level:2Challenge Level:2

Find the vertices of a pentagon given the midpoints of its sides.