Torsten Sillke, Apr, 7, 1993
Martin Gardner [*] says, there is a unique dissection of the square into
five congruent parts. ^^^^^^
Proof?
[*] MG5SA: The Unexpected Hanging and Other Mathematical Diversions
MG5SA: Simon & Schuster (1968)
MG5SA.15.5 Dissecting a Square
Question A:
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For which k does there exist a dissection of the n-dimensional hypercube into
k conguent connected parts which are not boxes?
In other words:
For which k do there exist subsets A_1, ..., A_n of the unit hypercube s.t.
i) all A_i open, connected
ii) the A_i are pairwise disjoined and congruent
iii) the closure of the union of the A_i is the hypercube
If 1