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 A packing exercise (Posted on 2018-09-14)
How can you assemble six 1 × 2 × 2 blocks and three 1 × 1 × 1 blocks into a 3 × 3 × 3 cube?

Source: Two Dutch architects: Jan Slothouber and William Graatsma.

 No Solution Yet Submitted by Ady TZIDON No Rating

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 solution | Comment 3 of 5 |
I had to have physical blocks in my hands to figure this out. Luckily I had saved a set of 29 (perhaps there had been 30 originally with one lost) small dice from the Science Materials Center's probability kit, from when I was a youngster. This was long enough ago that the address listed on the box was in New York, 3, NY, using postal zones prior to zip codes.

So I used a glue stick (so as to be temporary gluing) to make the 1x2x2 blocks.  Then I had to figure a way of presenting the result in a 2-D representation. I will present it layer by layer, with the 1x2x2 blocks labeled A, B, C, D, E and F, and the 1x1x1 blocks labeled a, b and c.

```a  A  A       D  D  E       D  D  E
B  A  A       B  b  E       F  F  E
B  C  C       B  C  C       F  F  c```

Clearly the 1x1x1 blocks lie on one body diagonal of the cube, with each face of the cube looking like the first or third of the above set of layers, having one 2x2 face of a 1x2x2 piece as well as the 1x2 edges of two other 1x2x2 pieces.

`a  A  A       A  E  E       E  D  D`
`B  A  A       A  E  E       E  F  F`
`B  C  C       C  C  c       c  F  F              C  C  c`
`              C  C  F                            B  B  F                                                        B  B  F                            B  B  F                            a  D  D                                                        a  D  D                            A  D  D                            A  E  E`

 Posted by Charlie on 2018-09-14 15:54:23

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