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Longest Pathology Puzzles By Size
This wiki page documents the longest known PP1 and PP2 puzzles which fit within small
Outside of trivial cases, these numbers should be considered lower bounds for the longest possible puzzles of various sizes.
To preview and play any of these levels, just copy the level data into the Pathology Level Creator
In PP1, all boxes can be pushed from all sides and there are no holes.
We have the following results for small PP1 puzzles:
2 | 3 | 4 | 5 | 6 | 7 | 8 | N | ||
---|---|---|---|---|---|---|---|---|---|
1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||
2 | 2 | 4 | 5 | 7 | 9 | 10 | 12 | ||
3 | 8 | 11 | 14 | 17 | 20 | 23 | |||
4 | 14 | 18 | 26 | 30 | 34 | ? | |||
5 | 34 | 40 | 46 | 54 | ? | ||||
6 | 47 | 55 | ? | ? | |||||
7 | 59 | ? | ? | ||||||
8 | ? | ? |
The results for rectangular boards with at most 25 spaces have been confirmed optimal by mathmasterzach by exhaustive computer search.
Trivial construction of the form: 40...03
40
03
413
000
4113
0000
For odd
41000
00013
For even
041000
020003
A lock with a long handle.
00...020
41...123
00...020
Two very different solutions, found by Flashback and dgriff24 respectively.
0410
0232
0220
0200
0314
2200
0020
2020
Expanded version of dgriff24's
11130
00422
01200
00201
3 More designs by davidspencer6174
00010
41023
01120
00020
00410
00232
02220
00200
02010
42023
00120
10020
By davidspencer6174.
000130
010422
011200
000201
Expanded version of davidspencer6174's
0000130
0110422
0111200
0000201
Expanded version of davidspencer6174's
00000130
01110422
01111200
00000201
02400
22220
02320
00100
10001
By davidspencer6174.
100000
001022
023200
022221
004101
By davidspencer6174.
0041000
0222210
0232010
0010100
1000000
By davidspencer6174.
02001000
12200010
42311110
02200010
00001000
By davidspencer6174
000001
012200
002310
142200
022001
020011
By davidspencer6174
0001020
0104220
0222200
0232001
0010011
1000111
By qqwref (based on the
0001020
0104220
0222200
0232001
0010011
1010111
1000111
We have the following results for small PP2 puzzles:
2 | 3 | 4 | 5 | 6 | 7 | 8 | N | ||
---|---|---|---|---|---|---|---|---|---|
1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||
2 | 2 | 4 | 6 | 10 | 16 | 19 | 24 | ||
3 | 10 | 16 | 32 | 46 | 56 | 70 | |||
4 | 30 | 58 | 104 | 110 | ? | ? | |||
5 | 118 | ? | ? | ? | ? | ||||
6 | 151 | ? | ? | ? | |||||
7 | 160 | 240 | ? | ||||||
8 | ? | ? |
The longest
The longest
sspenst provides a general construction for an
For
310000
552024
To scale this puzzle, insert
000
520
Between the last hole and the first box, ex.
310000 -> 310000000 -> 310000000000
552024 -> 555202024 -> 555520202024
For
3100000
5502024
The construction is similar to that of
For
31020050
55042020
For
31020005000
55540202020
The construction following
060
370
140
0413
0210
0255
By davidspencer6174 and mathmasterzach.
08555
0BH29
04535
By davidspencer6174 and mathmasterzach.
008555
01BH29
004535
By sspenst (based on the
0008555
011BH29
0004535
By sspenst
14000000
05979760
30600000
This pattern can be extended with additional alternating 7
and 9
columns to for a solution of length N^2 + 3N - 17
LifereaperX's 4x4 (attributed to ybbun).
5520
0020
11A0
3540
An alternative by davidspencer6174
5800
5320
7700
5460
mathmasterzach's starting position for part of kjs0722's R2
00000
00295
0B730
00465
sspenst's starting position for part of kjs0722's R2
580000
532DE0
57H000
546000
sspenst's modification of mathmasterzach's 4x7-106
0000565
0EC0735
00C0H75
1460585
00000
08020
02JA4
00837
06055
000050
022055
00D015
40B015
0BB215
000013
3555555
1111155
00004D0
00B0BD0
02B2B00
02020D0
0000000
Reach's Pathological Simplicity
55001111
31000011
11011224
10010010
10EE0010
10010000
11000111
The best known asymptotic growth for PP1 levels on an
The best known asymptotic growth for PP2 levels is exponential. One exponential construction is known: a modified version of Sokoban's exponential Fibo construction showcased by qqwref in Fibo.