| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
Is there a formula for the number of different connected
shapes which can be created with N squares on a grid? I wish
to consider only the uniquely different shapes. Thus the table
begins with:
# of squares # of shapes
1 1
2 1
3 2
4 5
I do not know whether there is a simple answer. By "connected",
I mean that at least one side of each square abuts a side of another
square and that all squares form one solid figure. You need not
concern yourselves with other space filling shapes (like trangles
or hexagons) unless the case of squares is too easy!
Dave Eklund
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 1076.1 | HERON::BUCHANAN | Andrew @vbo DTN 828-5805 | Tue May 09 1989 08:08 | 9 | |
In the literature, I think that these shapes are called 'animals'. Counting animals is a popular recreational pastime, but there are no explicit formulas known. It's the kind of thing (like number of graphs of order n, or number of groups of order n) which is very fiddly to compute in detail, but where some reasonable bounds can be established for large n without too much work. Regards, Andrew. | |||||
| 1076.2 | KOBAL::GILBERT | Ownership Obligates | Tue May 09 1989 11:16 | 27 | |
1 square, 1 shape X 2 squares, 1 share XX 3 squares, 2 shapes XXX XX X 4 squares, 5 shapes XXXX XXX XXX XX XX X X XX XX 5 squares, 11 shapes XXXXX XXXX XXXX XX X X X X X XX X X XXX XXX XXX XXX XXX XXX X X X X X X XXX XXX X | |||||
| 1076.3 | I thought there were 12 pentominos | POOL::HALLYB | The Smart Money was on Goliath | Tue May 09 1989 13:35 | 1 |
| 1076.4 | The twelfth pentaminoe | REGENT::PETERS | Chris Peters | Tue May 09 1989 13:47 | 9 |
Re: 1076.2 & .3
Yes, there are twelve pentaminoes. The one not listed in note 1076.2 is:
XX
XX
X
-- Chris Peters
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