Longest Rectangular PP1 Puzzles

This wiki page documents the longest known PP1 puzzles which fit within small $M \times N$ rectangles.

In PP1, all boxes can be pushed from all sides and there are no holes.

To preview and play any of these levels, just copy the level data into the Pathology Level Creator

	2	3	4	5	6	7	8	$\cdots$	N
1	1	2	3	4	5	6	7		$N - 1$
2	2	4	5	7	9	10	12		$\lfloor\frac{3N}{2}\rfloor$
3		8	11	14	17	20	23		$3 N - 1$
4			14	18	26	30	34		$4 (N + \lfloor\frac{N}{3}\rfloor) - 6$
5				34	40	46	54		?
6					49	59	65		?
7						67	78		?
8							90		?

The results for boards with at most 25 spaces have been confirmed optimal by mathmasterzach by exhaustive computer search.

$1 \times N$

Trivial construction of the form: 40...03

$2 \times 2$

40
03

$2 \times 3$

413
000

$2 \times 4$

4113
0000

$2 \times N$

For odd $N \geq 5$, the optimal is a zig-zag pattern.

41000
00013

For even $N > 5$, the optimal is a zig-zag pattern with a delaying block at the start.

041000
020003

$3 \times N$

A lock with a long handle.

00...020
41...123
00...020

$4 \times 4$

Two very different solutions, found by Flashback and dgriff24 respectively.

0410
0232
0220
0200

0314
2200
0020
2020

$4 \times 5$

Expanded version of dgriff24's $4 \times 4$

11130
00422
01200
00201

3 More designs created by hand by davidspencer6174

00010
41023
01120
00020

00410
00232
02220
00200

02010
42023
00120
10020

$4 \times 6$

Created by hand by davidspencer6174

000130
010422
011200
000201

$4 \times 7$

Expanded version of davidspencer6174's $4 \times 6$

0000130
0110422
0111200
0000201

$4 \times 8$

Expanded version of davidspencer6174's $4 \times 6$

00000130
01110422
01111200
00000201

$4 \times N$

The best we know so far is a continuation of the above pattern with "wiggles": Ex.

000000100000130
011110001110422
010001110001200
000100000100201

$5 \times 5$

Hem's hemlock (by hand)

02400
22220
02320
00100
10001

$5 \times 6$

Created by hand by davidspencer6174

100000
001022
023200
022221
004101

$5 \times 7$

Created by hand by davidspencer6174

0041000
0222210
0232010
0010100
1000000

$5 \times 8$

Created by hand by davidspencer6174

02001000
12200010
42311110
02200010
00001000

$6 \times 6$

Created by hand by Hem

100001
002200
022310
042200
122001
020011

$6 \times 7$

Created by hand by Hem

1010001
1224200
0022220
2002320
0220100
1000001

$6 \times 8$

Created by hand by Hem

10000111
00220011
02231001
04220200
12200220
02000020

$7 \times 7$

Created by hand by Hem

1110020
0200220
1220200
0422020
0223100
0022001
1000011

$7 \times 8$

Created by hand by Hem

0000110
0110022
0140220
0222200
0232000
0010220
1002022
1100000

$8 \times 8$

Hem's Boundary Unstable (by hand)

02000020
12200220
10220200
00022001
01002200
01142310
00112200
10000001