Visualising and representing

There are 575 NRICH Mathematical resources connected to Visualising and representing
Painting Cubes
problem

Painting cubes

Age
11 to 14
Challenge level
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Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?
A Tilted Square
problem

A tilted square

Age
14 to 16
Challenge level
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The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Knight's Swap
problem

Knight's swap

Age
7 to 11
Challenge level
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Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
Königsberg
problem

Königsberg

Age
11 to 14
Challenge level
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Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?
A Square in a Circle
problem

A square in a circle

Age
7 to 11
Challenge level
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What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?
Inside Out
problem

Inside out

Age
14 to 16
Challenge level
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There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you can colour every face of all of the smaller cubes?

Triangles within Triangles
problem

Triangles within triangles

Age
14 to 16
Challenge level
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Can you find a rule which connects consecutive triangular numbers?
Concrete wheel
problem

Concrete wheel

Age
11 to 14
Challenge level
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A huge wheel is rolling past your window. What do you see?
Clocking off
problem

Clocking off

Age
7 to 16
Challenge level
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I found these clocks in the Arts Centre at the University of Warwick intriguing - do they really need four clocks and what times would be ambiguous with only two or three of them?
One Out One Under
problem

One out one under

Age
14 to 16
Challenge level
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Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?