# Magna-Tease

Magna-Tease is a puzzle made by Skor-Mor Products in 1973. It consists of 12 red cubes with a magnet stuck on every face. The aim is to arrange them in a 3 by 12 rectangle, without any adjacent cubes' magnets repelling each other.

## The number of positions:

The 12 cubes can be ordered in 12! ways, and each has 24 orientations, giving 12!·2412 = 17,493,304,854,426,997,594,521,600 arrangements. This is an overestimate, since some cubes have identical magnet arrangements, and most cubes' magnet arrangements are symmetric. Furthermore this is of course not a realistic measure of difficulty, since you would never continue building if a cube already is repelled by a neighbour. Also, there are 156 solutions.

## Solution:

Most magnets have their North pole on the outside. There are however only 17 faces with a South pole. It just so happens that the 3 by 4 rectangle has exactly 17 touching faces, so every South pole must be used up by some adjacent pair.

There are four cubes that have only North pole magnets. These cubes can be easily recognised by testing all its faces against the face of another cube. All its magnets will behave the same way (all attract, or all repel). Once you have found one such all-North cube, you can use it to test all the faces of all the other cubes. You should find the following arrangements:

AmountPictureDescription
4No South poles
2One South pole
1Two South poles, on opposing faces
2Two South poles, on adjacent faces
3Three South poles

There are 156 solutions. Below is a complete list of them.

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