PENTOMINO 10x6 PUZZLE SOLUTIONS
Very briefly, pentominos are 12 different 2-dimensional or plane figures that
are formed by joining five equal-sized squares along their sides. Fitting the
12 figures or pieces together to form various-sized rectangles make for very
engaging puzzles. Rectanlges of 15x4, 12x5 and 10x6 are the most common puzzle
sizes but 10x6 is king.
10x6 puzzles are dealt with exclusively here. It is said that there are 2339
solutions to the 10x6 puzzle. Don't let that fool you, it takes plenty of time
and effort to find just one of those. IF you are good enough!
ONE 10x6 PENTOMINO SOULTION WITH THREE ADDITIONAL VARIATIONS
A A A P C C A A A P C C C C P A A A C C P A A A
A Z P P P C A Z P P P C C P P P Z A C P P P Z A
A Z Z P C C A Z Z P C C C C P Z Z A C C P Z Z A
S S Z Z K B S S Z Z T B S S Z Z K B S S Z Z T B
F S K K K B F S T T T B F S K K K B F S T T T B
F S S K T B F S S K T B F S S K T B F S S K T B
F F T T T B F F K K K B F F T T T B F F K K K B
F 6 2 2 T B F 6 2 2 K B F 6 2 2 T B F 6 2 2 K B
6 6 L 2 2 2 6 6 L 2 2 2 6 6 L 2 2 2 6 6 L 2 2 2
6 6 L L L L 6 6 L L L L 6 6 L L L L 6 6 L L L L
Both the green and yellow pieces (near the centers of each puzzle) have
been flipped (above and below each other). The top-most four pieces of
the two puzzles on the right have been reversed (left to right) relative
to the two on the left. Both of these changes have produced the 4 unique
puzzle solutions above.
See if you can figure out what the difference is between the second set
of four solutions (below) and the first set of 4 solutions above:
You guessed it! The very bottom 3 pieces (brown, indigo and violet) have
been rearranged in all 4 puzzles above. Though, rearranged, the 3 pieces
still retain the exact original overall outline. This now makes 8
different solutions of this basic puzzle.
ONE MORE 10x6 PENTOMINO SOULTION ALSO WITH THREE ADDITIONAL VARIATIONS
#1 #2 #3 #4
Notice the top half of all 4 puzzles (above) are identical! But each
bottom half is different. The bottom half of #2 is the mirror image of
the bottom half of #1. The bottom half of #3 is reversed from top to
bottom compared to #1. The bottom half of #4 was both flipped from left
to right as well as reversed from top to bottom. Another way of saying
it is the bottom half of #4 was rotated 180 degrees (either CW or CCW).
Each of these four solutions are different from each other, making 4
unique solutions. The bottom halves of these 4 solutions underwent
standard rotations and reflections (nothing real complicated) and
presto we now have 4 unique solutions instead of one!
In addition the top half can also be reversed and rotated (like the
bottom half was) generating a complete set of 4 unique top half parts.
Now each of the 4 new top parts can be paired up with each of the 4
existing bottom parts. 4 * 4 = 16. Yes! We can generate 16 unique
solutions, not just 4.
Still more: +--------+ +--------+
| TOP | | BOTTOM |
| HALF | | HALF |
+--------+ > Switch > +--------+
| BOTTOM | | TOP |
| HALF | | HALF |
+--------+ +--------+
Of these 16 new solutions everyone of the 16 top parts can be switched or
swapped with each bottom part. This yields a second set of 16 unique
solutions! This totals 32 (16 + 16) unique solutions.
Lastly, consider 2 different pairings of the same 2 pieces. In what way
are these two pairs the same?
The pair of puzzle pieces on the left (above) are the same as the 2 located
in the upper left hand corner of puzzles #1 to #4 pictured above.
The same 2 puzzle pieces on the right (above) have been switched. The green
piece was moved and the violet piece was flipped and rotated 90 degrees.
The overall outline or shape of both pairs is what is critical, they are the
same! The new pair on the right can perfectly replace the existing pair on
the left in all 32 solutions we have come up with so far. This gives us a
grand total of 64 (32 + 32) unique puzzle solutions!
PENTOMINO 10x6 PUZZLE SOLUTIONS
64 Unique but highly related pentomino solutions arranged in 8 rows of 8.
All 32 soultions in rows 1 to 4 of the 8 rows are in the same order as the
32 solutions in rows 5 to 8. The only difference between 32 solutions in
rows 1 to 4 and rows 5 to 8 are the top haves (of 6 pieces) have been
switched or swapped with the bottom halves (of 6 pieces).
The top and bottom halves were not reversed or rotated but only moved to
take each other's positions.
Row 1, #1 to #8
Row 2, #9 to #16
#9
| #10
| #11
| #12
| #13
| #14
| #15
| #16
|
Row 3, #17 to #24
#17
| #18
| #19
| #20
| #21
| #22
| #23
| #24
|
Row 4, #25 to #32
#25
| #26
| #27
| #28
| #29
| #30
| #31
| #32
|
Row 5, #33 to #40
#33
| #34
| #35
| #36
| #37
| #38
| #39
| #40
|
Row 6, #41 to #48
#41
| #42
| #43
| #44
| #45
| #46
| #47
| #48
|
Row 7, #49 to #54
#49
| #50
| #51
| #52
| #53
| #54
| #55
| #56
|
Row 8, #57 to #64
#57
| #58
| #59
| #60
| #61
| #62
| #63
| #64
|
A SHORT NOTE ABOUT COLOR IN GIF & HTML FILES:
COLOR TABLE - ROY G BIV (+6)
THREE GIF COLOR
ADDRESS BYTES
R G B
## ABBV COLOR 0D 0E 0F
--------------------------------- RGB - RED GREEN BLUE
1 RD RED FF 00 00 Hexadecimal Byte Values
2 OE ORANGE FF A5 00
3 YW YELLOW FF FF 00 2 Nibbles or 1 Byte gives
4 GN GREEN 00 B0 00 256 values for each RGB color.
5 BE BLUE 00 00 FF 3 Bytes make over 16 millIOn
6 IO INDIGO 80 00 80 colors.
7 VT VIOLET EE 82 EE
8 BK BLACK 00 00 00 2^24 = 16,777,216
9 GY GRAY A0 A0 A0
10 WE WHITE FF FF FF
11 BN BROWN C0 50 10
12 AA AQUA 00 FF FF
13 PK PINK FF D0 D0
---------------------------------
1 Red
2 Orange
3 Yellow
4 Green
5 Blue
6 Indigo
7 Violet
8 Black
9 Gray
10 White
11 Brown
12 Aqua
13 Pink
By JCShook 4/10/2021