15
$\begingroup$

Consider the following slanted pyramid which is made from 30 unit cubes:

Slanted pyramid. Level 1(bottom): 1x4x4 block, Level 2: 1x3x3 block, Level 3: 1x2x2 block, Level 4(top): 1x1x1 block

Step 1: Delete any 3 unit cubes. There is no restriction on which unit cubes are deleted. These 3 deleted unit cubes are no longer part of the puzzle.

Step 2: Dissect the reduced pyramid into pieces and rearrange the pieces to form a 3x3x3 cube.

This constructed cube will be made up of a number of pieces. The goal is to minimize the number of pieces in the cube.

Improve this question
$\endgroup$

1 Answer 1

Reset to default
20
$\begingroup$

You only need

two pieces!

Here's how:

Firstly, remove the three pieces marked with Xs in the image below.

diagram but with Xs

Then, separate it into two pieces: the ones marked with the line in the image below, and everything else remaining.

diagram with a line

That piece can then be placed on top of the green blocks to create a full 3x3x3 cube.
(You'll have to visualise this one, I don't have an image for it.)
This is obviously optimal as the puzzle cannot be done with only one piece, as a 3x3x3 subset of the original diagram does not exist.

Improve this answer
$\endgroup$
1
  • $\begingroup$ So elegant! Color those 5 pieces blue. $\endgroup$
    – z100
    Commented Nov 4 at 1:01

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.