Hi-Q or peg solitaire -- solutions to the game

When I was in the third grade (back in 1954), I had appendicitis and had to stay home from school for two weeks. During that time, I tried to solve the game Hi-Q backwards. I started with one peg in the middle, constructed a position that would lead to that, then one that would lead to that, and so forth until I reached the opening position. And I wrote down all the positions, so I could then play forward and win.

I just found my old, tattered notes, and figured -- what's the Internet for but to spread useful knowledge like this?

Another solution, from Erwin Engert, erengert@flashmail.com, November 10, 2002

I was much older when a fried of my parents gave me the game in 1967. I still have the game board and use it still.

I have over 400,000 solutions in total with the center peg missing. I have reduced one of my solution lists to 26 unique solutions, here is the first one. I also have a sample of two solutions for any peg missing for a start. As you can see I use a different numbering pattern for the peg location.

By starting with the center peg removed, which is the standard starting configuration. As the first move showes take the peg in hole 29, jump over the the peg in 24 and remove it then place the jumping peg in hole 17 which was empty at the start. Continue with the rest of the moves till the last peg ends back into hole 17.

           1 2 3
           4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
          28 29 30
          31 32 33

Solution 1
29 24 17
10 17 24
2   5 10
15 16 17
4   9 16
7   8   9
10   9   8
12 11 10
3   6 11
10 11 12
13 12 11
17 24 29
18 11   6
20 19 18
21 14   7
7   8   9
16   9   4
1   4   9
25 18 11
6 11 18
27 26 25
28 23 16
9 16 23
22 23 24
24 25 26
33 30 25
18 25 30
31 32 33
33 30 25
26 25 24
29 24 17

Still more solutions from Erwin Engert, erengert@flashmail.com, November 11, 2002

The first file has 26 solutions for the starting with the center hole empty.
The second file goes through a sample of two solutions for each of the 33 starting holes.

It just goes to prove any starting hole will produce a solution.

By the way, of all the solutions that I have for the starting center peg missing the last move will either end up in the center hole or by jumping the opposite direction you end up four holes from the center.

Starting with the center hole empty.

Starting with the center peg removed, which is the standard starting configuration, here are the results of testing the first 7 moves for every possible combination. There are a total of 55,246 moves. By taking each move forward by up to 1,000,000 moves it produced a total of 668 solutions. This is by no means to total number of solutions only a very small sample. It took the computer 63 hours to do all the testing to find the solutions. By removing all solutions that have the same move just in a different order, this further reduced the list to 26 final solutions that are listed below.

         1 2 3
         4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
        28 29 30
        31 32 33

Solution 1 -- see above

Solution 7
29 24 17
10 17 24
2   5 10
15 16 17
17 24 29
26 25 24
33 30 25
4   9 16
7   8   9
10   9   8
12 11 10
3   6 11
10 11 12
12 19 26
18 25 30
21 14   7
7   8   9
16   9   4
1   4   9
27 26 25
13 20 27
24 25 26
27 26 25
28 23 16
9 16 23
22 23 24
24 25 26
31 32 33
33 30 25
26 25 24
29 24 17

Solution 8
29 24 17
10 17 24
8   9 10
1   4   9
10   9   8
2   5 10
7   8   9
10   9   8
12 11 10
3   6 11
10 11 12
13 12 11
15 16 17
17 24 29
18 11   6
20 19 18
21 14   7
7   8   9
25 18 11
6 11 18
27 26 25
28 23 16
9 16 23
22 23 24
24 25 26
33 30 25
18 25 30
31 32 33
33 30 25
26 25 24
29 24 17

Solution 16
29 24 17
10 17 24
8   9 10
1   4   9
10   9   8
23 16   9
31 28 23
2   5 10
14 15 16
16   9   4
7   8   9
4   9 16
11 10   9
3   6 11
12 11 10
9 10 11
16 23 28
18 11   6
21 22 23
24 23 22
30 25 18
27 26 25
13 20 27
33 32 31
31 28 23
22 23 24
24 25 26
27 26 25
25 18 11
6 11 18
19 18 17

Solution 26
29 24 17
10 17 24
8   9 10
22 15   8
7   8   9
10   9   8
21 14   7
1   4   9
2   5 10
16   9   4
7   8   9
4   9 16
11 10   9
3   6 11
12 11 10
9 10 11
18 11   6
24 23 22
30 25 18
27 26 25
13 20 27
31 28 23
16 23 28
33 32 31
31 28 23
22 23 24
24 25 26
27 26 25
25 18 11
6 11 18
19 18 17

Solution 42
29 24 17
10 17 24
8   9 10
23 16   9
21 22 23
24 23 22
31 28 23
4   9 16
5 10 17
7 14 21
12 11 10
3   6 11
1   2   3
10 11 12
13 12 11
16 23 28
18 11   6
3   6 11
20 19 18
18 11   6
30 25 18
27 26 25
25 18 11
6 11 18
18 17 16
33 32 31
31 28 23
16 23 28
21 22 23
28 23 16
15 16 17

Solution 48
29 24 17
10 17 24
12 11 10
9 10 11
7   8   9
21 14   7
22 15   8
2   5 10
10 11 12
3   6 11
8   9 10
1   4   9
10   9   8
7   8   9
12 11 10
9 10 11
18 11   6
24 23 22
30 25 18
27 26 25
13 20 27
31 28 23
16 23 28
33 32 31
31 28 23
22 23 24
24 25 26
27 26 25
25 18 11
6 11 18
19 18 17

Solution 50
29 24 17
10 17 24
12 11 10
9 10 11
23 16   9
14 15 16
21 22 23
2   5 10
10 11 12
3   6 11
8   9 10
1   4   9
10   9   8
7   8   9
12 11 10
9 10 11
18 11   6
24 23 22
30 25 18
27 26 25
13 20 27
31 28 23
16 23 28
33 32 31
31 28 23
22 23 24
24 25 26
27 26 25
25 18 11
6 11 18
19 18 17

Solution 106
29 24 17
22 23 24
8 15 22
9 16 23
1   4   9
10   9   8
2   5 10
7   8   9
10   9   8
12 11 10
3   6 11
10 11 12
13 12 11
17 24 29
18 11   6
20 19 18
21 14   7
7   8   9
25 18 11
6 11 18
27 26 25
28 23 16
9 16 23
22 23 24
24 25 26
33 30 25
18 25 30
31 32 33
33 30 25
26 25 24
29 24 17

Solution 118
29 24 17
22 23 24
8 15 22
10   9   8
1   4   9
17 16 15
31 28 23
2   5 10
14 15 16
16   9   4
7   8   9
4   9 16
11 10   9
3   6 11
12 11 10
9 10 11
16 23 28
18 11   6
21 22 23
24 23 22
30 25 18
27 26 25
13 20 27
33 32 31
31 28 23
22 23 24
24 25 26
27 26 25
25 18 11
6 11 18
19 18 17

Solution 150
29 24 17
22 23 24
8 15 22
10   9   8
17 24 29
21 22 23
26 25 24
1   4   9
2   5 10
7 14 21
11 18 25
3   6 11
12 19 26
10 11 12
8   9 10
13 12 11
10 11 12
24 23 22
21 22 23
27 20 13
13 12 11
30 25 18
11 18 25
26 25 24
24 23 22
31 28 23
16 23 28
33 32 31
31 28 23
22 23 24
29 24 17

Solution 153
29 24 17
22 23 24
8 15 22
10   9   8
17 24 29
26 25 24
33 30 25
1   4   9
2   5 10
9 16 23
7   8   9
10   9   8
12 11 10
3   6 11
10 11 12
12 19 26
18 25 30
21 14   7
7   8   9
27 26 25
13 20 27
24 25 26
27 26 25
28 23 16
9 16 23
22 23 24
24 25 26
31 32 33
33 30 25
26 25 24
29 24 17

Solution 165
29 24 17
22 23 24
8 15 22
10   9   8
21 22 23
24 23 22
31 28 23
1   4   9
2   5 10
7 14 21
10 17 24
8   9 10
11 10   9
3   6 11
12 11 10
9 10 11
16 23 28
18 11   6
21 22 23
24 23 22
30 25 18
27 26 25
13 20 27
33 32 31
31 28 23
22 23 24
24 25 26
27 26 25
25 18 11
6 11 18
19 18 17

Solution 195
29 24 17
22 23 24
8 15 22
17 24 29
31 28 23
16 23 28
21 22 23
4   9 16
5 10 17
7 14 21
12 11 10
3   6 11
1   2   3
10 11 12
13 12 11
17 16 15
18 11   6
3   6 11
20 19 18
26 25 24
11 18 25
24 25 26
27 26 25
32 29 24
24 25 26
33 30 25
26 25 24
24 23 22
21 22 23
28 23 16
15 16 17

Solution 211
29 24 17
22 23 24
8 15 22
17 16 15
21 22 23
24 23 22
31 28 23
4   9 16
5 10 17
7 14 21
12 11 10
3   6 11
1   2   3
10 11 12
13 12 11
16 23 28
18 11   6
3   6 11
20 19 18
18 11   6
30 25 18
27 26 25
25 18 11
6 11 18
18 17 16
33 32 31
31 28 23
16 23 28
21 22 23
28 23 16
15 16 17

Solution 261
29 24 17
22 23 24
9 16 23
1   4   9
14 15 16
24 23 22
21 22 23
3   2   1
6   5   4
10 17 24
8   9 10
1   4   9
10   9   8
7   8   9
12 11 10
9 10 11
18 11   6
24 23 22
30 25 18
27 26 25
13 20 27
31 28 23
16 23 28
33 32 31
31 28 23
22 23 24
24 25 26
27 26 25
25 18 11
6 11 18
19 18 17

Solution 264
29 24 17
22 23 24
9 16 23
1   4   9
24 23 22
10 17 24
31 28 23
2   5 10
14 15 16
16   9   4
7   8   9
4   9 16
11 10   9
3   6 11
12 11 10
9 10 11
16 23 28
18 11   6
21 22 23
24 23 22
30 25 18
27 26 25
13 20 27
33 32 31
31 28 23
22 23 24
24 25 26
27 26 25
25 18 11
6 11 18
19 18 17

Solution 287
29 24 17
22 23 24
9 16 23
7   8   9
10   9   8
24 23 22
26 25 24
1   4   9
2   5 10
11 18 25
3   6 11
12 19 26
10 11 12
8   9 10
13 12 11
10 11 12
14 15 16
17 24 29
21 22 23
27 20 13
13 12 11
30 25 18
11 18 25
26 25 24
24 23 22
31 28 23
16 23 28
33 32 31
31 28 23
22 23 24
29 24 17

Solution 288
29 24 17
22 23 24
9 16 23
7   8   9
10   9   8
24 23 22
31 28 23
1   4   9
2   5 10
10 17 24
8   9 10
11 10   9
3   6 11
12 11 10
9 10 11
14 15 16
16 23 28
18 11   6
21 22 23
24 23 22
30 25 18
27 26 25
13 20 27
33 32 31
31 28 23
22 23 24
24 25 26
27 26 25
25 18 11
6 11 18
19 18 17

Solution 312
29 24 17
22 23 24
9 16 23
11 10   9
3   6 11
24 23 22
21 22 23
1   2   3
4   5   6
7 14 21
8   9 10
10 17 24
12 11 10
3   6 11
10 11 12
13 12 11
18 11   6
20 19 18
25 18 11
6 11 18
27 26 25
24 25 26
33 30 25
18 25 30
31 32 33
33 30 25
26 25 24
24 23 22
21 22 23
28 23 16
15 16 17

Solution 420
29 24 17
22 23 24
17 24 29
5 10 17
12 11 10
31 28 23
16 23 28
3   6 11
1   2   3
4   9 16
7   8   9
9 16 23
10 11 12
13 12 11
14 15 16
17 16 15
18 11   6
3   6 11
20 19 18
26 25 24
11 18 25
24 25 26
27 26 25
32 29 24
24 25 26
33 30 25
26 25 24
24 23 22
21 22 23
28 23 16
15 16 17

Solution 543
29 24 17
22 23 24
31 28 23
24 23 22
10 17 24
12 11 10
3   6 11
1   2   3
4   5   6
9 16 23
7   8   9
10 11 12
3   6 11
12 11 10
9 10 11
14 15 16
16 23 28
18 11   6
21 22 23
24 23 22
30 25 18
27 26 25
13 20 27
33 32 31
31 28 23
22 23 24
24 25 26
27 26 25
25 18 11
6 11 18
19 18 17

Solution 544
29 24 17
22 23 24
31 28 23
24 23 22
10 17 24
12 11 10
9 10 11
1   4   9
2   5 10
9 16 23
7   8   9
10 11 12
3   6 11
12 11 10
9 10 11
14 15 16
16 23 28
18 11   6
21 22 23
24 23 22
30 25 18
27 26 25
13 20 27
33 32 31
31 28 23
22 23 24
24 25 26
27 26 25
25 18 11
6 11 18
19 18 17

Solution 545
29 24 17
22 23 24
31 28 23
24 23 22
10 17 24
12 11 10
21 22 23
3   6 11
1   2   3
4   5   6
7 14 21
8 15 22
10 11 12
3   6 11
12 11 10
9 10 11
16 23 28
18 11   6
21 22 23
24 23 22
30 25 18
27 26 25
13 20 27
33 32 31
31 28 23
22 23 24
24 25 26
27 26 25
25 18 11
6 11 18
19 18 17

Solution 608
29 24 17
26 25 24
12 19 26
10 11 12
2   5 10
13 12 11
10 11 12
3   6 11
8   9 10
1   4   9
10   9   8
7   8   9
11 12 13
16   9   4
14 15 16
17 18 19
23 16   9
4   9 16
21 22 23
24 23 22
27 26 25
13 20 27
31 28 23
16 23 28
33 32 31
31 28 23
22 23 24
24 25 26
27 26 25
30 25 18
19 18 17

Solution 609
29 24 17
26 25 24
12 19 26
10 11 12
2   5 10
13 12 11
27 20 13
10 11 12
3   6 11
8   9 10
1   4   9
10   9   8
7   8   9
11 18 25
13 12 11
16   9   4
14 15 16
17 24 29
23 16   9
4   9 16
21 22 23
30 25 18
11 18 25
26 25 24
24 23 22
31 28 23
16 23 28
33 32 31
31 28 23
22 23 24
29 24 17

Two solutions for each of the 33 starting holes

Here is a sample of two different solutions for each possible starting puzzle with one pegs removed. No two solutions from a group have the same moves, just in a different order. Use the board layout found at the top of the first column. Start the game by removing the peg mentioned in the first line of each solution. The jumps are much like in checkers. The direction of jumping is vertical or horizontal. The fist number is the peg doing the jumping, the second number is jumped over and removed from the board. The third number is where the jumping peg lands. Make each of the moves as listed for that game.

         1 2 3
         4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
        28 29 30
        31 32 33

Remove peg 1
3   2   1
10   5   2
24 17 10
32 29 24
19 18 17
30 25 18
27 26 25
24 25 26
22 23 24
31 28 23
24 23 22
21 22 23
17 10   5
16 23 28
14 15 16
13 20 27
27 26 25
18 25 30
33 30 25
12 11 10
9 16 23
28 23 16
7   8   9
10   9   8
1   4   9
8   9 10
5 10 17
16 17 18
25 18 11
11   6   3
3   2   1

Remove peg 1
3   2   1
10   5   2
12 11 10
26 19 12
24 25 26
33 30 25
32 29 24
25 18 11
27 26 25
24 25 26
22 23 24
31 28 23
24 23 22
21 22 23
17 10   5
16 23 28
14 15 16
13 20 27
27 26 25
12 11 10
9 16 23
28 23 16
7   8   9
10   9   8
1   4   9
8   9 10
5 10 17
16 17 18
25 18 11
11   6   3
3   2   1

Remove peg 2
10   5   2
24 17 10
19 18 17
17 10   5
8   9 10
1   4   9
3   2   1
32 29 24
30 25 18
27 26 25
24 25 26
22 23 24
31 28 23
24 23 22
22 15   8
16   9   4
13 20 27
27 26 25
18 25 30
33 30 25
7   8   9
21 14   7
10   9   8
7   8   9
6 11 18
25 18 11
12 11 10
10   9   8
1   4   9
8   9 10
10   5   2

Remove peg 2
10   5   2
8   9 10
1   4   9
3   2   1
17 10   5
19 18 17
24 17 10
32 29 24
30 25 18
27 26 25
24 25 26
22 23 24
31 28 23
24 23 22
22 15   8
16   9   4
13 20 27
27 26 25
18 25 30
33 30 25
7   8   9
21 14   7
10   9   8
7   8   9
6 11 18
25 18 11
12 11 10
10   9   8
1   4   9
8   9 10
10   5   2

Remove peg 3
11   6   3
4   5   6
13 12 11
16   9   4
28 23 16
30 29 28
1   4   9
3   2   1
9 16 23
7   8   9
10 11 12
14 15 16
16   9   4
1   4   9
17 24 29
18 25 30
20 19 18
22 23 24
27 26 25
24 25 26
31 28 23
32 29 24
24 23 22
21 22 23
33 30 25
26 25 24
23 24 25
25 18 11
12 11 10
9 10 11
11   6   3

Remove peg 3
11   6   3
13 12 11
27 20 13
18 11   6
16 17 18
28 23 16
3   6 11
1   2   3
4   5   6
9 16 23
7   8   9
10 11 12
3   6 11
12 11 10
9 10 11
14 15 16
16 23 28
18 11   6
21 22 23
24 23 22
25 26 27
31 28 23
22 23 24
33 30 25
24 25 26
27 26 25
32 29 24
24 25 26
26 19 12
13 12 11
11   6   3

Remove peg 4
16   9   4
28 23 16
30 29 28
18 25 30
31 28 23
16 23 28
1   4   9
3   2   1
6   5   4
4   9 16
7   8   9
9 16 23
11 10   9
13 12 11
14 15 16
16   9   4
1   4   9
17 24 29
20 19 18
11 18 25
22 23 24
25 24 23
27 26 25
32 29 24
24 25 26
33 30 25
26 25 24
24 23 22
21 22 23
28 23 16
16   9   4

Remove peg 4
16   9   4
28 23 16
30 29 28
31 28 23
18 25 30
16 23 28
1   4   9
3   2   1
6   5   4
4   9 16
7   8   9
9 16 23
11 10   9
13 12 11
14 15 16
16   9   4
1   4   9
17 24 29
20 19 18
11 18 25
22 23 24
25 24 23
27 26 25
32 29 24
24 25 26
33 30 25
26 25 24
24 23 22
21 22 23
28 23 16
16   9   4

Remove peg 5
17 10   5
19 18 17
8   9 10
1   4   9
10   9   8
24 17 10
7   8   9
32 29 24
30 25 18
27 26 25
24 25 26
22 23 24
31 28 23
24 23 22
22 15   8
21 14   7
16   9   4
13 20 27
27 26 25
18 25 30
33 30 25
7   8   9
10   9   8
6 11 18
25 18 11
12 11 10
5 10 17
3   2   1
1   4   9
8   9 10
17 10   5

Remove peg 5
17 10   5
19 18 17
6 11 18
17 18 19
13 12 11
2   5 10
10 11 12
30 25 18
29 24 17
27 26 25
25 18 11
22 23 24
31 28 23
33 32 31
24 23 22
21 22 23
20 19 18
18 11   6
16 23 28
31 28 23
14 15 16
8   9 10
23 16   9
10   9   8
7   8   9
3   6 11
12 11 10
10   9   8
1   4   9
8   9 10
17 10   5

Remove peg 6
18 11   6
13 12 11
30 25 18
28 29 30
16 23 28
33 30 25
4   9 16
6   5   4
1   4   9
3   2   1
9 16 23
7   8   9
10 11 12
14 15 16
16   9   4
1   4   9
17 24 29
18 25 30
20 19 18
22 23 24
27 26 25
25 18 11
12 11 10
9 10 11
31 28 23
24 23 22
21 22 23
32 29 24
23 24 25
30 25 18
18 11   6

Remove peg 6
18 11   6
30 25 18
28 29 30
33 30 25
16 23 28
13 12 11
4   9 16
6   5   4
1   4   9
3   2   1
9 16 23
7   8   9
10 11 12
14 15 16
16   9   4
1   4   9
17 24 29
18 25 30
20 19 18
22 23 24
27 26 25
25 18 11
12 11 10
9 10 11
31 28 23
24 23 22
21 22 23
32 29 24
23 24 25
30 25 18
18 11   6

Remove peg 7
9   8   7
11 10   9
13 12 11
27 20 13
18 19 20
2   5 10
10 11 12
13 20 27
3   6 11
12 11 10
30 25 18
27 26 25
18 25 30
33 30 25
10   9   8
24 25 26
32 29 24
17 24 29
1   4   9
16   9   4
22 23 24
31 28 23
23 24 25
26 25 24
29 24 17
7   8   9
14 15 16
17 16 15
4   9 16
16 15 14
21 14   7

Remove peg 7
21 14   7
23 22 21
9 16 23
28 23 16
1   4   9
30 29 28
3   2   1
6   5   4
18 25 30
20 19 18
27 26 25
18 11   6
13 12 11
6 11 18
25 24 23
33 30 25
18 25 30
10 17 24
24 23 22
9 16 23
1   4   9
31 32 33
33 30 25
22 23 24
25 24 23
28 23 16
16   9   4
7   8   9
4   9 16
16 15 14
21 14   7

Remove peg 8
10   9   8
12 11 10
23 16   9
26 19 12
13 12 11
24 25 26
4   9 16
6   5   4
1   4   9
3   2   1
9 16 23
7   8   9
10 11 12
14 15 16
16   9   4
1   4   9
17 18 19
20 19 18
22 23 24
27 26 25
24 25 26
31 28 23
32 29 24
24 23 22
21 22 23
33 30 25
26 25 24
23 24 25
25 18 11
12 11 10
10   9   8

Remove peg 8
10   9   8
23 16   9
12 11 10
26 19 12
24 25 26
13 12 11
4   9 16
6   5   4
1   4   9
3   2   1
9 16 23
7   8   9
10 11 12
14 15 16
16   9   4
1   4   9
17 18 19
20 19 18
22 23 24
27 26 25
24 25 26
31 28 23
32 29 24
24 23 22
21 22 23
33 30 25
26 25 24
23 24 25
25 18 11
12 11 10
10   9   8

Remove peg 9
1   4   9
3   2   1
6   5   4
18 11   6
13 12 11
16 17 18
4   9 16
7   8   9
10 11 12
15 16 17
18 17 16
16   9   4
1   4   9
20 19 18
21 14   7
23 22 21
25 18 11
6 11 18
27 26 25
24 25 26
31 28 23
32 29 24
24 23 22
21 22 23
33 30 25
26 25 24
23 24 25
25 18 11
12 11 10
10   9   8
7   8   9

Remove peg 9
23 16   9
31 28 23
33 32 31
24 29 32
26 25 24
12 19 26
4   9 16
6   5   4
1   4   9
3   2   1
10 11 12
8   9 10
13 12 11
10 11 12
16 23 28
14 15 16
17 18 19
20 19 18
21 22 23
23 16   9
27 26 25
25 18 11
12 11 10
10   9   8
7   8   9
31 32 33
33 30 25
25 24 23
28 23 16
16   9   4
1   4   9

Remove peg 10
12 11 10
3   6 11
18 11   6
16 17 18
28 23 16
15 16 17
1   2   3
3   6 11
4   5   6
10 11 12
8   9 10
13 12 11
10 11 12
18 17 16
20 19 18
21 22 23
7 14 21
16 23 28
25 18 11
6 11 18
27 26 25
24 25 26
31 28 23
32 29 24
24 23 22
21 22 23
33 30 25
26 25 24
23 24 25
25 18 11
12 11 10

Remove peg 10
24 17 10
26 25 24
11 18 25
30 25 18
23 24 25
21 22 23
3   6 11
1   2   3
4   5   6
7 14 21
8 15 22
10   9   8
12 11 10
3   6 11
10 11 12
12 19 26
18 25 30
22 23 24
27 26 25
13 20 27
24 25 26
27 26 25
31 28 23
32 29 24
24 25 26
33 30 25
26 25 24
24 23 22
21 22 23
23 16   9
8   9 10

Remove peg 11
3   6 11
1   2   3
4   5   6
16   9   4
7   8   9
21 14   7
4   9 16
11 10   9
3   6 11
12 11 10
9 10 11
16 15 14
7 14 21
18 11   6
20 19 18
17 18 19
26 19 12
13 12 11
6 11 18
24 25 26
22 23 24
27 26 25
24 25 26
31 28 23
32 29 24
24 23 22
21 22 23
33 30 25
26 25 24
23 24 25
25 18 11

Remove peg 11
25 18 11
33 30 25
28 29 30
30 25 18
11 18 25
13 12 11
6 11 18
4   5   6
3   6 11
1   2   3
10 11 12
8   9 10
16 23 28
14 15 16
17 10   5
18 25 30
20 19 18
21 22 23
23 16   9
27 26 25
25 18 11
12 11 10
10   9   8
7   8   9
31 32 33
33 30 25
25 24 23
28 23 16
16   9   4
4   5   6
3   6 11

Remove peg 12
10 11 12
3   6 11
8   9 10
22 15   8
17 16 15
14 15 16
1   2   3
4   5   6
7   8   9
10   9   8
12 11 10
3   6 11
10 11 12
13 12 11
18 11   6
20 19 18
23 16   9
8   9 10
25 18 11
6 11 18
27 26 25
24 25 26
31 28 23
32 29 24
24 23 22
21 22 23
33 30 25
26 25 24
23 24 25
25 18 11
10 11 12

Remove peg 12
26 19 12
24 25 26
22 23 24
9 16 23
7   8   9
21 14   7
4   9 16
6   5   4
1   4   9
3   2   1
10   9   8
7   8   9
11 18 25
13 12 11
16   9   4
1   4   9
24 17 10
10 11 12
26 25 24
23 24 25
27 20 13
13 12 11
31 28 23
32 29 24
24 25 26
33 30 25
26 25 24
24 23 22
22 15   8
8   9 10
10 11 12

Remove peg 13
11 12 13
3   6 11
18 11   6
16 17 18
28 23 16
15 16 17
1   2   3
3   6 11
4   5   6
10 11 12
8   9 10
13 12 11
10 11 12
18 17 16
20 19 18
21 22 23
7 14 21
16 23 28
25 18 11
6 11 18
27 26 25
24 25 26
31 28 23
32 29 24
24 23 22
21 22 23
33 30 25
26 25 24
23 24 25
25 18 11
11 12 13

Remove peg 13
27 20 13
25 26 27
23 24 25
21 22 23
12 19 26
26 25 24
7 14 21
8 15 22
10 11 12
2   5 10
3   6 11
10   9   8
1   4   9
8   9 10
11 18 25
13 12 11
10 11 12
16 17 18
24 25 26
22 23 24
27 26 25
24 25 26
31 28 23
32 29 24
24 23 22
21 22 23
33 30 25
26 25 24
23 24 25
25 18 11
11 12 13

Remove peg 14
16 15 14
18 17 16
5 10 17
17 16 15
28 23 16
21 22 23
7 14 21
20 19 18
12 11 10
3   6 11
18 11   6
30 25 18
27 26 25
18 25 30
30 29 28
24 23 22
1   2   3
3   6 11
10 11 12
13 12 11
31 28 23
33 32 31
16 23 28
31 28 23
8   9 10
11 10   9
4   9 16
16 23 28
21 22 23
28 23 16
16 15 14

Remove peg 14
16 15 14
28 23 16
21 22 23
7 14 21
17 16 15
5 10 17
18 17 16
20 19 18
12 11 10
3   6 11
18 11   6
30 25 18
27 26 25
18 25 30
30 29 28
24 23 22
1   2   3
3   6 11
10 11 12
13 12 11
31 28 23
33 32 31
16 23 28
31 28 23
8   9 10
11 10   9
4   9 16
16 23 28
21 22 23
28 23 16
16 15 14

Remove peg 15
17 16 15
5 10 17
28 23 16
21 22 23
16 23 28
18 17 16
31 28 23
20 19 18
12 11 10
3   6 11
18 11   6
30 25 18
27 26 25
18 25 30
30 29 28
33 32 31
24 23 22
1   2   3
3   6 11
10 11 12
13 12 11
31 28 23
16 23 28
8   9 10
11 10   9
4   9 16
15 16 17
7 14 21
21 22 23
28 23 16
17 16 15

Remove peg 15
17 16 15
5 10 17
8   9 10
17 10   5
1   4   9
14 15 16
16   9   4
12 11 10
19 18 17
3   6 11
11 10   9
30 25 18
27 26 25
13 20 27
18 25 30
33 30 25
2   5 10
10   9   8
24 25 26
27 26 25
32 29 24
28 23 16
25 24 23
16 23 28
31 28 23
7   8   9
4   9 16
16 23 28
21 22 23
28 23 16
17 16 15

Remove peg 16
4   9 16
7   8   9
10   9   8
23 16   9
24 17 10
31 28 23
5 10 17
8   9 10
10 17 24
12 11 10
3   6 11
1   2   3
10 11 12
13 12 11
14 15 16
16 23 28
18 11   6
3   6 11
20 19 18
18 11   6
21 22 23
24 23 22
30 25 18
27 26 25
25 18 11
6 11 18
33 32 31
31 28 23
22 23 24
29 24 17
18 17 16

Remove peg 16
28 23 16
30 29 28
31 28 23
33 32 31
16 23 28
31 28 23
4   9 16
6   5   4
1   4   9
3   2   1
16   9   4
1   4   9
14 15 16
16   9   4
7   8   9
4   9 16
11 10   9
13 12 11
16   9   4
17 24 29
18 11   6
20 19 18
25 18 11
6 11 18
27 26 25
18 25 30
30 29 28
28 23 16
21 22 23
23 16   9
4   9 16

Remove peg 17
5 10 17
8   9 10
1   4   9
10   9   8
7   8   9
12 11 10
10   9   8
23 16   9
8   9 10
17 10   5
31 28 23
2   5 10
3   6 11
10 11 12
13 12 11
14 15 16
16 23 28
18 11   6
20 19 18
21 22 23
23 28 31
25 18 11
6 11 18
27 26 25
24 25 26
33 30 25
18 25 30
31 32 33
33 30 25
26 25 24
29 24 17

Remove peg 17
19 18 17
30 25 18
28 29 30
33 30 25
18 25 30
16 23 28
6 11 18
13 12 11
10 11 12
24 17 10
4   9 16
31 32 33
33 30 25
27 20 13
26 25 24
21 22 23
24 23 22
15 16 17
18 17 16
13 12 11
11 10   9
16   9   4
7 14 21
21 22 23
28 23 16
1   4   9
16   9   4
3   2   1
1   4   9
8   9 10
5 10 17

Remove peg 18
6 11 18
4   5   6
3   6 11
16   9   4
17 10   5
28 23 16
1   2   3
4   5   6
7   8   9
9 16 23
12 11 10
3   6 11
10 11 12
13 12 11
14 15 16
16 23 28
18 11   6
20 19 18
21 22 23
24 23 22
25 18 11
6 11 18
27 26 25
31 28 23
22 23 24
25 24 23
32 29 24
33 30 25
18 25 30
23 24 25
30 25 18

Remove peg 18
30 25 18
23 24 25
31 28 23
10 17 24
12 11 10
5 10 17
3   6 11
1   2   3
8   9 10
10 11 12
13 12 11
16 23 28
14 15 16
17 16 15
18 11   6
3   6 11
20 19 18
18 11   6
21 22 23
24 23 22
22 15   8
7   8   9
4   9 16
33 32 31
31 28 23
16 23 28
28 29 30
30 25 18
27 26 25
25 18 11
6 11 18

Remove peg 19
17 18 19
29 24 17
6 11 18
13 12 11
18 11   6
16 17 18
3   6 11
14 15 16
22 23 24
31 28 23
16 23 28
4   9 16
7   8   9
16   9   4
4   5   6
1   2   3
10 11 12
33 32 31
31 28 23
24 23 22
21 22 23
3   6 11
18 11   6
26 25 24
23 24 25
30 25 18
19 18 17
27 20 13
13 12 11
6 11 18
17 18 19

Remove peg 19
17 18 19
29 24 17
26 25 24
17 24 29
33 30 25
20 19 18
18 25 30
22 23 24
15 16 17
31 28 23
23 24 25
4   9 16
7   8   9
21 14   7
16   9   4
1   4   9
32 29 24
24 25 26
10   9   8
7   8   9
2   5 10
6 11 18
9 10 11
18 11   6
3   6 11
27 26 25
30 25 18
18 11   6
13 12 11
6 11 18
17 18 19

Remove peg 20
18 19 20
16 17 18
29 24 17
17 18 19
6 11 18
13 12 11
27 20 13
14 15 16
22 23 24
31 28 23
16 23 28
4   9 16
7   8   9
16   9   4
4   5   6
10 11 12
33 32 31
31 28 23
24 23 22
21 22 23
3   6 11
1   2   3
18 11   6
3   6 11
26 25 24
23 24 25
30 25 18
18 11   6
13 12 11
6 11 18
18 19 20

Remove peg 20
18 19 20
6 11 18
13 12 11
27 20 13
17 18 19
29 24 17
16 17 18
14 15 16
22 23 24
31 28 23
16 23 28
4   9 16
7   8   9
16   9   4
4   5   6
10 11 12
33 32 31
31 28 23
24 23 22
21 22 23
3   6 11
1   2   3
18 11   6
3   6 11
26 25 24
23 24 25
30 25 18
18 11   6
13 12 11
6 11 18
18 19 20

Remove peg 21
7 14 21
16 15 14
4   9 16
17 16 15
5 10 17
21 14   7
7   8   9
12 11 10
3   6 11
1   2   3
10 11 12
13 12 11
18 11   6
3   6 11
20 19 18
17 18 19
22 15   8
8   9 10
10 11 12
24 23 22
26 25 24
12 19 26
27 26 25
24 25 26
31 28 23
32 29 24
23 24 25
26 25 24
33 30 25
25 24 23
23 22 21

Remove peg 21
23 22 21
8 15 22
10   9   8
12 11 10
25 18 11
33 30 25
1   4   9
3   2   1
6   5   4
9 16 23
1   4   9
10 11 12
8   9 10
13 12 11
10 11 12
20 19 18
17 18 19
28 23 16
21 22 23
7 14 21
16 23 28
25 24 23
27 26 25
12 19 26
26 25 24
24 23 22
21 22 23
32 29 24
24 23 22
31 28 23
23 22 21

Remove peg 22
24 23 22
9 16 23
7   8   9
26 25 24
11 18 25
20 19 18
3   6 11
1   2   3
4   5   6
10   9   8
12 11 10
3   6 11
10 11 12
13 12 11
14 15 16
17 18 19
23 16   9
8   9 10
10 11 12
12 19 26
21 22 23
24 23 22
26 25 24
31 28 23
33 30 25
24 25 26
22 23 24
27 26 25
25 24 23
32 29 24
24 23 22

Remove peg 22
24 23 22
26 25 24
12 19 26
10 11 12
3   6 11
18 11   6
1   2   3
3   6 11
4   5   6
6 11 18
8   9 10
13 12 11
10 11 12
17 18 19
15 16 17
20 19 18
17 18 19
21 22 23
7 14 21
23 24 25
26 25 24
12 19 26
27 26 25
24 25 26
31 28 23
32 29 24
24 23 22
21 22 23
33 30 25
26 25 24
24 23 22

Remove peg 23
9 16 23
1   4   9
3   2   1
6   5   4
17 10   5
18 11   6
4   9 16
6   5   4
1   4   9
8   9 10
13 12 11
10 11 12
15 16 17
20 19 18
17 18 19
28 23 16
21 22 23
7 14 21
16 23 28
25 24 23
27 26 25
12 19 26
26 25 24
23 24 25
31 28 23
32 29 24
24 25 26
33 30 25
26 25 24
24 23 22
21 22 23

Remove peg 23
31 28 23
33 32 31
24 29 32
22 23 24
8 15 22
10   9   8
1   4   9
2   5 10
9 16 23
7   8   9
10   9   8
12 11 10
3   6 11
10 11 12
13 12 11
17 24 29
18 11   6
20 19 18
21 14   7
7   8   9
22 23 24
25 18 11
6 11 18
27 26 25
24 25 26
31 32 33
33 30 25
26 25 24
29 24 17
18 17 16
9 16 23

Remove peg 24
22 23 24
8 15 22
10   9   8
12 11 10
25 18 11
33 30 25
1   4   9
3   2   1
6   5   4
9 16 23
1   4   9
10 11 12
8   9 10
13 12 11
10 11 12
20 19 18
17 18 19
28 23 16
21 22 23
7 14 21
16 23 28
25 24 23
27 26 25
12 19 26
26 25 24
24 23 22
21 22 23
32 29 24
24 23 22
31 28 23
22 23 24

Remove peg 24
26 25 24
33 30 25
24 25 26
10 17 24
15 16 17
12 11 10
3   6 11
1   2   3
4   5   6
10 11 12
3   6 11
8   9 10
11 18 25
13 12 11
10 11 12
20 19 18
17 18 19
28 23 16
21 22 23
7 14 21
16 23 28
25 24 23
27 26 25
12 19 26
26 25 24
24 23 22
21 22 23
32 29 24
24 23 22
31 28 23
22 23 24

Remove peg 25
11 18 25
3   6 11
16 17 18
18 11   6
28 23 16
29 24 17
1   2   3
3   6 11
4   5   6
6 11 18
9 10 11
7   8   9
9 16 23
12 11 10
10 17 24
14 15 16
16 23 28
19 18 17
17 24 29
21 22 23
26 25 24
24 23 22
31 28 23
22 23 24
33 30 25
24 25 26
27 26 25
13 20 27
32 29 24
24 25 26
27 26 25

Remove peg 25
33 30 25
31 32 33
23 28 31
9 16 23
18 17 16
7   8   9
5 10 17
6 11 18
13 12 11
16 23 28
4   9 16
18 11   6
3   6 11
1   2   3
16 17 18
14 15 16
18 11   6
3   6 11
20 19 18
18 11   6
21 22 23
24 23 22
31 28 23
22 23 24
29 24 17
16 17 18
25 18 11
6 11 18
27 26 25
18 25 30
33 30 25

Remove peg 26
12 19 26
10 11 12
2   5 10
3   6 11
18 11   6
9 10 11
1   4   9
6 11 18
8   9 10
13 12 11
10 11 12
17 18 19
15 16 17
20 19 18
17 18 19
28 23 16
21 22 23
7 14 21
16 23 28
25 24 23
27 26 25
12 19 26
26 25 24
24 23 22
21 22 23
32 29 24
24 23 22
31 28 23
22 23 24
33 30 25
24 25 26

Remove peg 26
24 25 26
22 23 24
9 16 23
7   8   9
21 14   7
4   9 16
6   5   4
1   4   9
3   2   1
10   9   8
7   8   9
11 18 25
13 12 11
16   9   4
1   4   9
20 19 18
17 18 19
24 23 22
22 15   8
8   9 10
10 11 12
26 25 24
12 19 26
27 26 25
24 25 26
31 28 23
32 29 24
23 24 25
26 25 24
33 30 25
24 25 26

Remove peg 27
25 26 27
23 24 25
21 22 23
7 14 21
16 15 14
32 29 24
24 23 22
21 14   7
31 28 23
22 23 24
4   9 16
7   8   9
16   9   4
1   4   9
24 25 26
10   9   8
2   5 10
17 10   5
33 30 25
18 25 30
12 11 10
3   6 11
11 10   9
8   9 10
5 10 17
27 26 25
20 19 18
17 18 19
30 25 18
18 19 20
13 20 27

Remove peg 27
13 20 27
11 12 13
25 18 11
6 11 18
9 10 11
2   5 10
7   8   9
21 14   7
22 15   8
23 24 25
31 28 23
16 23 28
4   9 16
7   8   9
16   9   4
1   4   9
32 29 24
17 10   5
25 24 23
28 23 16
16   9   4
33 30 25
18 11   6
3   6 11
4   5   6
6 11 18
18 25 30
27 26 25
30 25 18
18 19 20
13 20 27

Remove peg 28
16 23 28
21 22 23
4   9 16
6   5   4
18 11   6
1   4   9
30 25 18
28 29 30
33 30 25
31 32 33
25 18 11
27 26 25
24 23 22
20 19 18
18 25 30
33 30 25
17 10   5
16   9   4
14 15 16
12 11 10
7   8   9
9 16 23
22 23 24
25 24 23
3   6 11
10 11 12
13 12 11
2   5 10
11 10   9
4   9 16
16 23 28

Remove peg 28
16 23 28
4   9 16
6   5   4
1   4   9
18 11   6
21 22 23
30 25 18
28 29 30
33 30 25
31 32 33
25 18 11
27 26 25
24 23 22
20 19 18
18 25 30
33 30 25
17 10   5
16   9   4
14 15 16
12 11 10
7   8   9
9 16 23
22 23 24
25 24 23
3   6 11
10 11 12
13 12 11
2   5 10
11 10   9
4   9 16
16 23 28

Remove peg 29
17 24 29
15 16 17
26 25 24
33 30 25
24 25 26
10 17 24
27 26 25
2   5 10
4   9 16
7   8   9
10   9   8
12 11 10
3   6 11
10 11 12
12 19 26
13 20 27
18 25 30
21 14   7
7   8   9
16   9   4
1   4   9
27 26 25
24 25 26
28 23 16
9 16 23
22 23 24
29 24 17
31 32 33
33 30 25
26 25 24
17 24 29

Remove peg 29
17 24 29
15 16 17
28 23 16
17 16 15
21 22 23
32 29 24
24 23 22
4   9 16
5 10 17
7   8   9
9 16 23
12 11 10
3   6 11
1   2   3
10 11 12
13 12 11
14 15 16
16 23 28
18 11   6
3   6 11
20 19 18
26 25 24
11 18 25
24 25 26
27 26 25
31 28 23
22 23 24
24 25 26
33 30 25
26 25 24
17 24 29

Remove peg 30
18 25 30
6 11 18
9 10 11
1   4   9
3   2   1
12 11 10
9 10 11
7   8   9
11 18 25
16   9   4
1   4   9
14 15 16
16   9   4
4   5   6
20 19 18
17 18 19
26 19 12
13 12 11
6 11 18
24 25 26
22 23 24
27 26 25
24 25 26
31 28 23
32 29 24
24 23 22
21 22 23
33 30 25
26 25 24
23 24 25
18 25 30

Remove peg 30
28 29 30
17 24 29
22 23 24
9 16 23
24 23 22
7   8   9
4   9 16
5 10 17
12 11 10
3   6 11
1   2   3
10 11 12
13 12 11
18 11   6
3   6 11
16 17 18
14 15 16
18 11   6
20 19 18
21 22 23
16 23 28
25 18 11
6 11 18
27 26 25
31 28 23
32 29 24
24 25 26
33 30 25
26 25 24
23 24 25
18 25 30

Remove peg 31
23 28 31
9 16 23
14 15 16
23 16   9
4   9 16
17 16 15
5 10 17
7   8   9
12 11 10
3   6 11
1   2   3
10 11 12
13 12 11
18 11   6
3   6 11
20 19 18
17 18 19
21 22 23
24 23 22
22 15   8
8   9 10
10 11 12
26 25 24
12 19 26
27 26 25
24 25 26
33 30 25
26 25 24
31 32 33
24 29 32
33 32 31

Remove peg 31
33 32 31
24 29 32
22 23 24
17 24 29
8 15 22
10   9   8
1   4   9
2   5 10
9 16 23
7   8   9
10   9   8
12 11 10
3   6 11
10 11 12
13 12 11
18 11   6
20 19 18
21 14   7
7   8   9
22 23 24
25 18 11
6 11 18
27 26 25
24 25 26
31 32 33
33 30 25
26 25 24
29 24 17
18 17 16
9 16 23
23 28 31

Remove peg 32
24 29 32
10 17 24
15 16 17
17 24 29
26 25 24
33 30 25
31 32 33
2   5 10
4   9 16
7   8   9
10   9   8
12 11 10
3   6 11
10 11 12
12 19 26
18 25 30
21 14   7
7   8   9
16   9   4
1   4   9
27 26 25
13 20 27
24 25 26
27 26 25
28 23 16
9 16 23
22 23 24
24 25 26
33 30 25
26 25 24
24 29 32

Remove peg 32
24 29 32
26 25 24
33 30 25
31 32 33
17 24 29
15 16 17
10 17 24
2   5 10
4   9 16
7   8   9
10   9   8
12 11 10
3   6 11
10 11 12
12 19 26
18 25 30
21 14   7
7   8   9
16   9   4
1   4   9
27 26 25
13 20 27
24 25 26
27 26 25
28 23 16
9 16 23
22 23 24
24 25 26
33 30 25
26 25 24
24 29 32

Remove peg 33
31 32 33
24 29 32
10 17 24
2   5 10
15 16 17
4   9 16
7   8   9
10   9   8
12 11 10
3   6 11
10 11 12
13 12 11
17 24 29
18 11   6
20 19 18
21 14   7
7   8   9
16   9   4
1   4   9
22 23 24
25 18 11
6 11 18
27 26 25
24 25 26
33 30 25
26 25 24
29 24 17
18 17 16
9 16 23
23 28 31
31 32 33

Remove peg 33
31 32 33
24 29 32
22 23 24
17 24 29
8 15 22
10   9   8
1   4   9
2   5 10
9 16 23
7   8   9
10   9   8
12 11 10
3   6 11
10 11 12
13 12 11
18 11   6
20 19 18
21 14   7
7   8   9
22 23 24
25 18 11
6 11 18
27 26 25
24 25 26
33 30 25
26 25 24
29 24 17
18 17 16
9 16 23
23 28 31
31 32 33


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Hi-Q (or Peg Solitaire) -- A solution to the game

Another solution, from Erwin Engert, erengert@flashmail.com, November 10, 2002

Still more solutions from Erwin Engert, erengert@flashmail.com, November 11, 2002

Starting with the center hole empty.

Two solutions for each of the 33 starting holes