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Cubic Conundrum

Age 7 to 16
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The solution below has the cubes in this slightly different order:

Cube A Cube B Cube C
Cube D Cube E Cube F

Correct solutions to the first part of the question were received from: Alastair H (Forres Academy), Andrei L (School 205, Bucharest). The solution below is based on Andrei's submission. Well done to both of you.

First I created a small cube from the net in the figure and observed the cubes from the problem:

The first cube cannot be formed from that net, because the square marked with a red arrow should be in the position marked with a blue arrow:

Looking at the cube made from the net: It is possible to see that the second cube (horizontally) can be made from that net and also the last three

In conclusion, the 4 cubes denominated before are the same one, created from the net (B, D, E and F below).

The second part of the problem:

First shade the three faces of the view B of the cube which are not visible. Then do the same with the other three views of the same cube (D,E and F).

Cube A

A Cube BB Cube CC Cube DD Cube EE CUbe FF

You end up shading all the faces. This means that you can see all the faces of the cube in the four views B, D, E and F so there are no hidden faces where you can shade additional sections.

 


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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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