Dividing along the gridlines, divide an NxN square in to the maximum number of pieces, such that each piece is unique (including rotations and reflections.) Solve for N<=8. For example, for N=3, you can divide a 3x3 square into four pieces of sizes (3,3,2,1).
Source: Original.
[Update 24Sept2008: Submitted
this sequence to the OEIS:
http://www.research.att.com/~njas/sequences/A144876]
Bernie Erickson has this summary:
Shapes can be formed: 1 one, 1 two, 2 threes, 5 fours, and 12 fives.
The series then: 1, 2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, . . .
The running sum: 1, 3, 6, 9, 13, 17, 21, 25, 29, 34, 35, 39, 44, 49, 54, 59, 64, . . .
Square numbers in the series fit inside: 1, 6, 9, 17, 25, 39, 49, 64, . . .
Maximal candidates are: 1, 6 - 2, 9, 17 - 1, 25, 39 - 3, 49, 64
Note that with three of the eight N x N squares, a larger piece is needed but can be offset by just one smaller piece taken away.
Candidates
1 Piece, 1 x 1: 1
2 Pieces, 2 x 2: 1, 3
4 Pieces, 3 x 3: 1, 2, 3, 3
5 Pieces, 4 x 4: 2, 3, 3, 4, 4
8 Pieces, 5 x 5: 1, 2, 3, 3, 4, 4, 4, 4
10 Pieces, 6 x 6: 1, 2, 3, 4, 4, 4, 4, 4, 5, 5
13 Pieces, 7 x 7: 1, 2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5
16 Pieces, 8 x 8: 1, 2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5
All the candidates check out.
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