Here is the library of all partitions (up to isomorphisms) of [75], no block has an arithmetic progression of length 3.

Solution 1 is :
B1: 6 7 9 14 18 20 23 24 36 38 43 44 46 51 55 57 60 61 73 75
B2: 4 5 12 22 26 28 29 31 37 41 42 49 59 63 65 66 68 74
B3: 1 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72
B4: 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70

Solution 2 is :
B1: 6 7 9 14 18 20 23 24 36 38 43 44 46 51 55 57 60 61 73
B2: 4 5 12 22 26 28 29 31 37 41 42 49 59 63 65 66 68 74
B3: 1 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72
B4: 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70 75

Solution 3 is :
B1: 6 7 9 14 18 20 23 24 36 38 43 44 46 51 55 57 60 61 73
B2: 4 5 12 22 26 28 29 31 37 41 42 49 59 63 65 66 68 74 75
B3: 1 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72
B4: 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70

Solution 4 is :
B1: 6 7 9 14 18 20 23 24 36 38 43 44 46 51 55 57 60 61 73
B2: 4 5 12 22 26 28 29 31 37 41 42 49 59 63 65 66 68 74
B3: 1 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72 75
B4: 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70

Solution 5 is :
B1: 6 7 9 14 18 20 23 24 36 38 43 44 46 51 55 57 60 61 73
B2: 4 5 12 22 26 28 29 31 37 41 42 49 59 63 65 66 68 74
B3: 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72
B4: 1 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70 75

Solution 6 is :
B1: 6 7 9 14 18 20 23 24 36 38 43 44 46 51 55 57 60 61 73
B2: 4 5 12 22 26 28 29 31 37 41 42 49 59 63 65 66 68 74
B3: 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72 75
B4: 1 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70

Solution 7 is :
B1: 6 7 9 14 18 20 23 24 36 38 43 44 46 51 55 57 60 61 73
B2: 4 5 12 22 26 28 29 31 37 41 42 49 59 63 65 66 68 74 75
B3: 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72
B4: 1 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70

Solution 8 is :
B1: 6 7 9 14 18 20 23 24 36 38 43 44 46 51 55 57 60 61 73 75
B2: 4 5 12 22 26 28 29 31 37 41 42 49 59 63 65 66 68 74
B3: 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72
B4: 1 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70

Solution 9 is :
B1: 6 7 9 14 18 20 23 24 36 38 43 44 46 51 55 57 60 61 73
B2: 1 4 5 12 22 26 28 29 31 37 41 42 49 59 63 65 66 68 74 75
B3: 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72
B4: 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70

Solution 10 is :
B1: 6 7 9 14 18 20 23 24 36 38 43 44 46 51 55 57 60 61 73 75
B2: 1 4 5 12 22 26 28 29 31 37 41 42 49 59 63 65 66 68 74
B3: 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72
B4: 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70

Solution 11 is :
B1: 6 7 9 14 18 20 23 24 36 38 43 44 46 51 55 57 60 61 73
B2: 1 4 5 12 22 26 28 29 31 37 41 42 49 59 63 65 66 68 74
B3: 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72
B4: 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70 75

Solution 12 is :
B1: 6 7 9 14 18 20 23 24 36 38 43 44 46 51 55 57 60 61 73
B2: 1 4 5 12 22 26 28 29 31 37 41 42 49 59 63 65 66 68 74
B3: 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72 75
B4: 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70

Solution 13 is :
B1: 1 6 7 9 14 18 20 23 24 36 38 43 44 46 51 55 57 60 61 73
B2: 4 5 12 22 26 28 29 31 37 41 42 49 59 63 65 66 68 74
B3: 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72
B4: 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70 75

Solution 14 is :
B1: 1 6 7 9 14 18 20 23 24 36 38 43 44 46 51 55 57 60 61 73
B2: 4 5 12 22 26 28 29 31 37 41 42 49 59 63 65 66 68 74
B3: 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72 75
B4: 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70

Solution 15 is :
B1: 1 6 7 9 14 18 20 23 24 36 38 43 44 46 51 55 57 60 61 73
B2: 4 5 12 22 26 28 29 31 37 41 42 49 59 63 65 66 68 74 75
B3: 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72
B4: 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70

Solution 16 is :
B1: 4 5 12 22 26 28 29 31 37 38 41 42 49 59 63 65 66 68 74
B2: 1 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72 75
B3: 6 7 9 14 18 20 23 24 36 43 44 46 51 55 57 60 61 73
B4: 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70

Solution 17 is :
B1: 4 5 12 22 26 28 29 31 37 38 41 42 49 59 63 65 66 68 74
B2: 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72 75
B3: 6 7 9 14 18 20 23 24 36 43 44 46 51 55 57 60 61 73
B4: 1 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70

Solution 18 is :
B1: 4 5 12 22 26 28 29 31 37 38 41 42 49 59 63 65 66 68 74
B2: 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72 75
B3: 1 6 7 9 14 18 20 23 24 36 43 44 46 51 55 57 60 61 73
B4: 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70

Solution 19 is :
B1: 1 4 5 12 22 26 28 29 31 37 38 41 42 49 59 63 65 66 68 74
B2: 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72 75
B3: 6 7 9 14 18 20 23 24 36 43 44 46 51 55 57 60 61 73
B4: 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70

Solution 20 is :
B1: 4 5 12 22 26 28 29 31 37 38 41 42 49 59 63 65 66 68 74
B2: 1 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72
B3: 6 7 9 14 18 20 23 24 36 43 44 46 51 55 57 60 61 73 75
B4: 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70

Solution 21 is :
B1: 4 5 12 22 26 28 29 31 37 38 41 42 49 59 63 65 66 68 74
B2: 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72
B3: 6 7 9 14 18 20 23 24 36 43 44 46 51 55 57 60 61 73 75
B4: 1 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70

Solution 22 is :
B1: 1 4 5 12 22 26 28 29 31 37 38 41 42 49 59 63 65 66 68 74
B2: 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72
B3: 6 7 9 14 18 20 23 24 36 43 44 46 51 55 57 60 61 73 75
B4: 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70

Solution 23 is :
B1: 4 5 12 22 26 28 29 31 37 38 41 42 49 59 63 65 66 68 74
B2: 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72
B3: 1 6 7 9 14 18 20 23 24 36 43 44 46 51 55 57 60 61 73 75
B4: 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70

Solution 24 is :
B1: 1 4 5 12 22 26 28 29 31 37 38 41 42 49 59 63 65 66 68 74
B2: 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72
B3: 6 7 9 14 18 20 23 24 36 43 44 46 51 55 57 60 61 73
B4: 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70 75

Solution 25 is :
B1: 4 5 12 22 26 28 29 31 37 38 41 42 49 59 63 65 66 68 74
B2: 1 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72
B3: 6 7 9 14 18 20 23 24 36 43 44 46 51 55 57 60 61 73
B4: 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70 75

Solution 26 is :
B1: 4 5 12 22 26 28 29 31 37 38 41 42 49 59 63 65 66 68 74
B2: 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72
B3: 1 6 7 9 14 18 20 23 24 36 43 44 46 51 55 57 60 61 73
B4: 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70 75

Solution 27 is :
B1: 4 5 12 22 26 28 29 31 37 38 41 42 49 59 63 65 66 68 74
B2: 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72
B3: 6 7 9 14 18 20 23 24 36 43 44 46 51 55 57 60 61 73
B4: 1 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70 75

Solution 28 is :
B1: 4 5 12 22 26 28 29 31 37 38 41 42 49 59 63 65 66 68 74 75
B2: 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72
B3: 1 6 7 9 14 18 20 23 24 36 43 44 46 51 55 57 60 61 73
B4: 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70

Solution 29 is :
B1: 4 5 12 22 26 28 29 31 37 38 41 42 49 59 63 65 66 68 74 75
B2: 1 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72
B3: 6 7 9 14 18 20 23 24 36 43 44 46 51 55 57 60 61 73
B4: 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70

Solution 30 is :
B1: 4 5 12 22 26 28 29 31 37 38 41 42 49 59 63 65 66 68 74 75
B2: 2 8 10 11 13 17 27 34 35 39 45 47 48 50 54 64 71 72
B3: 6 7 9 14 18 20 23 24 36 43 44 46 51 55 57 60 61 73
B4: 1 3 15 16 19 21 25 30 32 33 40 52 53 56 58 62 67 69 70

Last modified: March 11, 2003