# A straight forward Geometrical question !

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This question has five parts and needs five answers

Cut a cube of side 2 cms into eight identical pieces such that the surface area of each piece is :

A.  6 sq cms
B.  4 + 22 sq cms
C.  5 + 22 sq cms
D.  10 sq cms
E.   6 + 24.25 sq cms

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Spoiler

A. would be 8 1x1x1 cm cubes. That should be the smallest possible surface area for 8 pieces.

Anything bigger can be done by cutting 4 1x1x2 cm pieces, and then cutting a symmetric comb joint. There are multiple answers. Do your solutions result in the fewest possible faces, or only convex pieces? Or some extra symmetry? Or min number of planar cuts?

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Why is this straightforward question a brain teaser or puzzle?

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1 hour ago, md65536 said:
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A. would be 8 1x1x1 cm cubes. That should be the smallest possible surface area for 8 pieces.

Anything bigger can be done by cutting 4 1x1x2 cm pieces, and then cutting a symmetric comb joint. There are multiple answers. Do your solutions result in the fewest possible faces, or only convex pieces? Or some extra symmetry? Or min number of planar cuts?

Similarly all other Cuts are Planar and no Curve/convex or Concave surface needed.

Correct Cuts and dimensions to be revealed.

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Spoiler

B. Cut like layer cake into 2 layers, then cut top with an X, corner to corner.

C. Cut like a pizza into 8 slices, starting corner to corner.

D. Cut like layer cake into 8 layers.

E. Cut into 4 layers, and then each layer into a wedge, cutting from one edge to the farthest opposite edge.

You can change the area continuously for some of these cuts just by rotating the cube, so I still suspect there might be some with multiple answers.

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I found some ranges where you can create pieces of any area in the range, but none of them overlap at any of the values of A through E. Was that on purpose? Because, I found some other possible areas of pieces, including one that has 2 different answers.

So I'll extend the puzzle with these...

Cut a cube of side 2 cms into eight identical pieces such that the surface area of each piece is :

F: 7 sq cms

G: 6 + 2 sq cms

H: 5 + 5 sq cms

Then bonus: For which pairs of A through H is it possible to create 8 identical pieces with a surface area anywhere in between the two? Based on that answer, how would you cut one cube into 8 identical pieces of surface area a, and cut another cube into 8 identical pieces also of surface a but with a different shape than those from the first cube?

I'm not certain that I haven't made any errors here!

Edited by md65536
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• 3 months later...
On 1/7/2023 at 2:51 PM, md65536 said:
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B. Cut like layer cake into 2 layers, then cut top with an X, corner to corner.

C. Cut like a pizza into 8 slices, starting corner to corner.

D. Cut like layer cake into 8 layers.

E. Cut into 4 layers, and then each layer into a wedge, cutting from one edge to the farthest opposite edge.

You can change the area continuously for some of these cuts just by rotating the cube, so I still suspect there might be some with multiple answers.

On 1/7/2023 at 2:51 PM, md65536 said:
Hide contents

B. Cut like layer cake into 2 layers, then cut top with an X, corner to corner.

C. Cut like a pizza into 8 slices, starting corner to corner.

D. Cut like layer cake into 8 layers.

E. Cut into 4 layers, and then each layer into a wedge, cutting from one edge to the farthest opposite edge.

You can change the area continuously for some of these cuts just by rotating the cube, so I still suspect there might be some with multiple answers.

On 1/7/2023 at 2:51 PM, md65536 said:
Hide contents

B. Cut like layer cake into 2 layers, then cut top with an X, corner to corner.

C. Cut like a pizza into 8 slices, starting corner to corner.

D. Cut like layer cake into 8 layers.

E. Cut into 4 layers, and then each layer into a wedge, cutting from one edge to the farthest opposite edge.

You can change the area continuously for some of these cuts just by rotating the cube, so I still suspect there might be some with multiple answers.

I think you are absolutely right

Well done

If there is any error I will report after studying

Bcoz my answers while creating the puzzle was  with similar solutions in mind

Great Show !

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2 hours ago, Commander said:

I think you are absolutely right

Well done

If there is any error I will report after studying

Bcoz my answers while creating the puzzle were with similar solutions in mind

Great Show !

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