Saturday, January 24, 2009

Hypercube 4p

Although by superimposing two reference points we have seen that compartments 5 and 9 occupy the same vertical path, the user will find it impossible to enter compartment 9 directly from compartment 5.

Stepping back now from the joining of these two compartments, we will see that a remainder of the cube has been blocked off by the maneuver required to link 5 and 4.

This now isolated compartment (9) can be expressed as the sum of the two surrounding it.

4 + 4 + 5 + 5 = 18 = 1 + 8 = 9

As seen above, from within compartments 5 and 4 there is no entrance to compartment 9. But its contents may be inferred from what is present in 5 and 4, and from what can be felt and heard through the walls.

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