Examples of 5-tuples of elements of S_6 from whose elements one can form exactly k distinct products in which every factor occurs exactly once: k = 1: (), (1,2), (3,4), (1,2)(3,4), (5,6) k = 2: (), (1,2), (3,4), (1,2)(3,4), (4,5) k = 3: (), (2,3), (2,3,4), (3,4), (5,6) k = 4: (), (1,2), (1,2)(3,4), (2,3), (3,4) k = 5: (), (1,2), (2,3), (2,3,4), (5,6) k = 6: (), (1,2), (2,3), (3,4), (2,3)(5,6) k = 7: (), (1,2)(3,4), (1,2,3,4), (2,4), (3,4) k = 8: (), (1,2)(3,4), (1,2,3,4), (2,4), (4,5) k = 9: (), (2,3), (2,3,4), (3,4), (4,5) k = 10: (), (1,2), (2,3), (3,4), (3,4,5) k = 11: (), (1,2), (2,3), (3,4), (1,2,3,4) k = 12: (), (1,2)(3,4), (1,2,3,4), (2,4), (3,4,5) k = 13: (), (1,2), (2,3), (3,4), (2,3,5,4) k = 14: (), (2,3), (2,3,4), (3,4), (3,5)(4,6) k = 15: (), (1,2), (2,3), (3,4), (2,4,3,5) k = 16: (), (1,2), (2,3), (3,4), (2,3,4,5) k = 17: (), (1,2), (2,3), (3,4), (2,4,5) k = 18: (), (1,2), (2,3), (3,4), (2,5)(4,6) k = 19: (), (1,2), (2,3), (2,3,4), (2,3,4,5) k = 20: (), (1,2), (2,3), (2,3,4), (2,3,5)(4,6) k = 21: (), (1,2), (2,3), (2,3,4), (2,5)(4,6) k = 22: (), (1,2), (2,3), (2,3,4), (2,5)(3,6,4) k = 23: (), (1,2), (2,3), (2,4), (2,5)(3,4,6) k = 24: (), (1,2), (2,3), (2,4), (2,5) k = 25: (1,2), (1,2,3,4), (2,3,4), (2,4,3), (4,5) k = 26: (1,2), (1,2,3,4), (2,3,4), (2,4,3), (2,4,5,3) k = 27: (1,2), (1,2,3,4), (2,3,4), (2,4,3), (3,4,5) k = 28: (1,2), (1,2,3,4), (2,3,4), (2,4,3), (3,5,4) k = 29: (1,2), (1,2,3,4), (2,3,4), (2,4,3), (2,3,5) k = 30: (1,2), (1,2,3,4), (2,3,4), (2,4,3), (2,3)(4,5) k = 31: (1,2), (1,2,3,4), (2,3,4), (2,4,3), (2,5,3) k = 32: (1,2), (1,2,3,4), (2,3,4), (2,4,3), (1,3,5,4,2) k = 33: (1,2), (1,2,3,4), (2,3,4), (2,4,3), (2,5,4) k = 34: (1,2), (1,2,3,4), (2,3,4), (2,4,3), (3,5)(4,6) k = 35: (1,2), (1,2,3,4), (2,3,4), (2,4,3), (2,4,6,3,5) k = 36: (1,2), (1,2,3,4), (2,3,4), (2,4,3), (1,2,5,4,3) k = 37: (1,2), (1,2,3,4), (2,3,4), (2,4,3), (1,2,5)(3,4) k = 38: (1,2), (1,2,3,4), (2,3,4), (2,4,3), (2,3,5)(4,6) k = 39: (1,2), (1,2,3,4), (2,3,4), (2,4,3), (2,5,3)(4,6) k = 40: (1,2), (1,2,3,4), (2,3,4), (2,4,3), (2,5)(3,4,6) k = 41: (1,2), (1,2,3,4), (2,3,4), (2,4,3), (2,5)(4,6) k = 42: (1,2), (1,2,3,4), (2,3,4), (2,4,3), (1,2,3,5)(4,6) k = 43: (1,2), (1,2,3,4), (2,3,4), (2,4,3), (1,2,5)(3,6) k = 44: (1,2), (1,2,3,4), (2,3,4), (2,4,3), (1,3,6,2,5) k = 45: (1,2), (1,2,3,4), (2,3,4), (2,4,3), (1,2,5)(4,6) k = 46: (1,2), (1,2,3,4), (2,3,4), (2,4,3), (1,5)(4,6) k = 47: (1,2), (1,2,3), (1,5), (2,3,4), (2,3,5)(4,6) k = 48: (1,2), (2,3), (2,3,4), (2,4,3), (3,5)(4,6) k = 49: (1,2), (2,3), (2,3,4), (3,4), (2,5,3)(4,6) k = 50: (1,2), (2,3), (2,3,4), (3,4), (2,4,6,3,5) k = 51: (1,2), (2,3), (2,3,4), (3,4), (2,3,5)(4,6) k = 52: (1,2), (2,3), (2,3,4), (3,4), (2,5,3,6,4) k = 53: (1,2), (2,3), (2,3,4), (2,4,3), (2,4,6,3,5) k = 54: (1,2), (2,3), (2,3,4), (2,4,3), (2,3,5)(4,6) k = 55: (1,2), (2,3), (2,3,4), (2,4,3), (1,3,4,6,2,5) k = 56: (1,2), (2,3), (2,3,4), (2,4,3), (2,5)(4,6) k = 57: (1,2), (1,2)(3,4), (2,3), (2,3,4), (1,2,5)(4,6) k = 58: (1,2), (2,3), (2,3,4), (2,4,3), (2,5)(3,4,6) k = 59: (1,2), (1,2)(3,4), (2,3), (2,3,4), (2,3,5)(4,6) k = 60: (1,2), (1,2)(3,4), (2,3), (2,3,4), (2,5,3,6,4) k = 61: (1,2), (1,2)(3,4), (2,3), (2,3,4), (2,5)(3,6,4) k = 62: (1,2), (1,2)(3,4), (2,3), (2,3,4), (1,5,2)(3,6) k = 63: (1,2), (1,2)(3,4), (2,3), (2,3,4), (2,5)(3,6) k = 64: (1,2), (1,2,3), (1,5), (2,3,4), (2,4)(3,5,6) k = 65: (1,2), (1,2,3), (2,4,3), (2,4), (2,3,5)(4,6) k = 66: (1,2), (1,2)(3,4), (2,3), (2,4), (1,5)(3,4,6) k = 67: (1,2), (1,2,3), (2,4,3), (2,4), (2,5,3,6,4) k = 68: (1,2), (1,2,3), (2,4,3), (2,4), (2,5,3)(4,6) k = 69: (1,2), (1,2)(3,4), (2,3), (2,4), (1,2,5)(4,6) k = 70: (1,2), (1,2)(3,4), (2,3), (2,4), (1,3,4,6,2,5) k = 71: (1,2), (1,2)(3,4), (2,3), (2,4), (2,3,5)(4,6) k = 72: (1,2), (1,2)(3,4), (2,3), (2,4), (1,3,5)(2,4,6) k = 73: (1,2), (1,2,3), (2,4,3), (2,4), (1,5,2,6,4,3) k = 74: (1,2), (1,2,3), (2,4,3), (2,4), (2,5)(3,6) k = 75: (1,2), (1,2,3), (1,5), (2,3,4), (1,3,6)(2,4,5) k = 76: (1,2), (1,2,3), (1,5), (2,3,4), (1,2,4)(3,6,5) k = 77: (1,2), (1,2,3), (1,5), (2,3,4), (2,6)(3,4,5) k = 78: (1,2), (1,2)(3,4), (2,3), (2,4), (2,5)(4,6) k = 79: (1,2,3), (1,2,3,4), (1,5), (2,3,4), (3,6,5,4) k = 80: (1,2,3), (1,2,3,4), (1,5), (2,3,4), (2,6,3,4,5) k = 81: (1,2,3), (1,2,3,4), (1,5), (2,3,4), (3,6)(4,5) k = 82: (1,2,3), (1,2,3,4), (1,5), (2,3,4), (2,6)(3,4,5) k = 83: (1,2,3), (1,2,3,4), (1,5), (2,3,4), (1,3,4,5,2,6) k = 84: (1,2,3), (1,2,3,4), (1,5), (2,3,4), (1,2)(3,6,4,5) k = 85: (1,2,3), (1,2,3,4), (1,5), (2,3), (1,6)(3,4) k = 86: (1,2)(3,4), (1,2,3,4), (1,2,4,3), (1,5), (2,6,3,4,5) k = 87: (1,2)(3,4), (1,2,3,4), (1,2,4,3), (1,5), (1,2)(4,6,5) k = 88: (1,2)(3,4), (1,2,3,4), (1,2,4,3), (1,5), (1,3,6,2,4,5) k = 89: (1,2)(3,4), (1,2,3,4), (1,2,4,3), (1,5), (2,5,3,4,6) k = 90: (1,2)(3,4), (1,2,3,4), (1,2,4,3), (1,5), (2,3,5,4,6) k = 91: (1,2)(3,4), (1,2,3,4), (1,2,4,3), (1,5), (1,3,5,6,2,4) k = 92: (1,2)(3,4), (1,2,3,4), (1,2,4,3), (1,5), (1,6)(2,3,5,4) k = 93: (1,2)(3,4), (1,2,3,4), (1,2,4,3), (1,5), (1,6,2)(4,5) k = 94: (1,2)(3,4), (1,2,3,4), (1,2,4,3), (1,5), (1,6,4,5,2) k = 95: (1,2), (1,2,3), (1,2,3,4), (1,5), (2,6)(4,5) k = 96: (1,2)(3,4), (1,2,3,4), (1,2,4,3), (1,5), (2,6)(3,4,5) k = 97: (1,2,3,4), (1,2,4,3), (1,3,2,4), (1,5), (2,4)(3,5,6) k = 98: (1,2,3,4), (1,2,4,3), (1,3,2,4), (1,5), (2,3,5)(4,6) k = 99: (1,2,3,4), (1,2,4,3), (1,3,2,4), (1,5), (2,6,4,5,3) k = 100: (1,2,3,4), (1,2,4,3), (1,3,2,4), (1,5), (1,2)(3,6,4,5) k = 101: (1,2,3,4), (1,2,4,3), (1,3,2,4), (1,5), (1,3,5,2,4,6) k = 102: (1,2,3,4), (1,2,4,3), (1,3,2,4), (1,5), (1,2,5,3,4,6) k = 103: (1,2,3), (1,2,3,4), (1,5)(3,4), (2,4,3), (1,3,5,4,2,6) k = 104: (1,2)(3,4), (1,3), (1,4), (1,5), (1,3,6,4)(2,5) k = 105: (1,2)(4,5), (1,5)(4,6), (2,3,5), (2,4), (3,4) k = 106: (1,2)(3,4), (1,3), (1,4), (1,5), (1,6)(2,5) k = 107: (1,2,3), (1,2,3,4), (1,5)(3,4), (2,4,3), (1,6)(2,4,5,3) k = 108: (1,2,3), (1,2,3,4), (1,5)(3,4), (2,4,3), (1,6)(3,5,4) k = 109: (1,2,3), (1,2,3,4), (1,5)(3,4), (2,4,3), (1,6)(3,5) k = 110: (1,2,3,4), (1,3)(5,6), (2,5), (3,5), (4,5) k = 111: (1,2)(4,5), (1,3,4)(2,6), (2,3,4,5), (2,3,5,4), (2,4,3,5) k = 112: (1,2)(3,4), (1,2,3,4), (1,4)(2,6)(3,5), (2,5,3,4), (2,5)(3,4) k = 113: (1,2)(4,5), (1,2,3,4), (1,4)(5,6), (2,5), (3,5) k = 114: (1,2,3,5), (1,2,4)(3,5), (1,3)(4,5), (1,6,2,5), (2,3)(4,5), k = 115: (1,2)(3,4,5), (1,3)(4,5), (1,5,6)(3,4), (2,4)(3,5), (2,5) k = 116: (1,2,3,4), (1,2,3,5,4), (1,5)(2,6), (2,3,4), (2,5)(3,4) k = 117: ? k = 118: (1,2)(3,4,5), (1,3)(4,5), (1,2,5,6), (2,4)(3,5), (2,5) k = 119: ? k = 120: (1,2), (1,3), (1,4), (1,5), (1,6)