Много интересна задачка, наистина. Благодаря ти!
Доста трудоемка е и аз бих я започнал като питам за 2 от 7 топки с 3 тегления....
Пращам ти решение за 13 топки с 4 тегления

Balls: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 (inclusive 2 - different )

1: 0, 1, 2, 3 < 4, 5, 6, 7
2: 0, 4, 5 < 6, 8, 9
3: 0, 7 < 10, 11
4: 0 < 10 // result = (6, 10)
4: 0 = 10 // result = (6, 11)
4: 0 > 10 // !!! impossible
3: 0, 7 = 10, 11
4: 8 < 9 // result = (6, 9)
4: 8 = 9 // result = (6, 12)
4: 8 > 9 // result = (6, 8)
3: 0, 7 > 10, 11
4: 6 < 8 // result = (7, 8)
4: 6 = 8 // result = (7, 9)
4: 6 > 8 // result = (6, 7)
2: 0, 4, 5 = 6, 8, 9
3: 4 < 5
4: 6 < 8 // result = (5, 8)
4: 6 = 8 // result = (5, 9)
4: 6 > 8 // result = (5, 6)
3: 4 = 5
4: 10 < 11 // result = (7, 11)
4: 10 = 11 // result = (7, 12)
4: 10 > 11 // result = (7, 10)
3: 4 > 5
4: 6 < 8 // result = (4, 8)
4: 6 = 8 // result = (4, 9)
4: 6 > 8 // result = (4, 6)
2: 0, 4, 5 > 6, 8, 9
3: 4, 7 < 5, 10
4: 10 < 11 // result = (5, 11)
4: 10 = 11 // result = (5, 12)
4: 10 > 11 // result = (5, 10)
3: 4, 7 = 5, 10
4: 4 < 5 // result = (5, 7)
4: 4 = 5 // result = (4, 5)
4: 4 > 5 // result = (4, 10)
3: 4, 7 > 5, 10
4: 7 < 11 // result = (4, 11)
4: 7 = 11 // result = (4, 12)
4: 7 > 11 // result = (4, 7)
1: 0, 1, 2, 3 = 4, 5, 6, 7
2: 0, 1, 2 < 3, 4, 8
3: 3, 9 < 4, 8
4: 10 < 11 // result = (8, 11)
4: 10 = 11 // result = (8, 12)
4: 10 > 11 // result = (8, 10)
3: 3, 9 = 4, 8
4: 0 < 3 // result = (3, 4)
4: 0 = 3 // result = (8, 9)
4: 0 > 3 // !!! impossible
3: 3, 9 > 4, 8
4: 5 < 6 // result = (3, 6)
4: 5 = 6 // result = (3, 7)
4: 5 > 6 // result = (3, 5)
2: 0, 1, 2 = 3, 4, 8
3: 4 < 9
4: 10 < 11 // result = (9, 11)
4: 10 = 11 // result = (9, 12)
4: 10 > 11 // result = (9, 10)
3: 4 = 9
4: 10 < 11 // result = (11, 12)
4: 10 = 11 // result = (10, 11)
4: 10 > 11 // result = (10, 12)
3: 4 > 9
4: 0 < 1 // result = (1, 4)
4: 0 = 1 // result = (2, 4)
4: 0 > 1 // result = (0, 4)
2: 0, 1, 2 > 3, 4, 8
3: 0 < 1
4: 5 < 6 // result = (1, 6)
4: 5 = 6 // result = (1, 7)
4: 5 > 6 // result = (1, 5)
3: 0 = 1
4: 5 < 6 // result = (2, 6)
4: 5 = 6 // result = (2, 7)
4: 5 > 6 // result = (2, 5)
3: 0 > 1
4: 5 < 6 // result = (0, 6)
4: 5 = 6 // result = (0, 7)
4: 5 > 6 // result = (0, 5)
1: 0, 1, 2, 3 > 4, 5, 6, 7
2: 0, 1, 4 < 2, 8, 9
3: 0, 3 < 10, 11
4: 0 < 10 // result = (2, 10)
4: 0 = 10 // result = (2, 11)
4: 0 > 10 // !!! impossible
3: 0, 3 = 10, 11
4: 8 < 9 // result = (2, 9)
4: 8 = 9 // result = (2, 12)
4: 8 > 9 // result = (2, 8)
3: 0, 3 > 10, 11
4: 2 < 8 // result = (3, 8)
4: 2 = 8 // result = (3, 9)
4: 2 > 8 // result = (2, 3)
2: 0, 1, 4 = 2, 8, 9
3: 0 < 1
4: 2 < 8 // result = (1, 8)
4: 2 = 8 // result = (1, 9)
4: 2 > 8 // result = (1, 2)
3: 0 = 1
4: 10 < 11 // result = (3, 11)
4: 10 = 11 // result = (3, 12)
4: 10 > 11 // result = (3, 10)
3: 0 > 1
4: 2 < 8 // result = (0, 8)
4: 2 = 8 // result = (0, 9)
4: 2 > 8 // result = (0, 2)
2: 0, 1, 4 > 2, 8, 9
3: 0, 3 < 1, 10
4: 10 < 11 // result = (1, 11)
4: 10 = 11 // result = (1, 12)
4: 10 > 11 // result = (1, 10)
3: 0, 3 = 1, 10
4: 0 < 1 // result = (1, 3)
4: 0 = 1 // result = (0, 1)
4: 0 > 1 // result = (0, 10)
3: 0, 3 > 1, 10
4: 3 < 11 // result = (0, 11)
4: 3 = 11 // result = (0, 12)
4: 3 > 11 // result = (0, 3)