яко решение /а ако е и вярно ;)))//

не съм очаквал че може така лесно да се изпише решение на задачата...

проверих 2-3 варианта - наистина действа!
мързи ме да проверявам за повече

Съдържаниет е скрито
Влезте за да го видите

Вярно е. Обаче с 2 по-тежки топки задачата е за хрупачи.
Очевидно е, че мин. ходове са:
F = log3(N над M)
Понеже са цели - стават H = ceil( F ), където:
N - топки, M - po-тежки, ceil - най-малко int, по-голямо от аргумента.

Интересното става, когато F клони отдолу към H. За 2 ot 13 - F=3.965647....
По този път лесно ще си намериш "интересните" комбинации. Например 3 от 12 (F=4.909491...)
И за да не дървенея - ето ти разписано решение за 3 от 12 с 5 хода:

Balls: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 (inclusive 3 - different )
All combinations: 220
1: 0, 1, 2 < 3, 4, 5 // possibilities: 73 [(0, 3, 4), (0, 3, 5), (0, 4, 5), (1, 3, 4), (1, 3, 5), (1, 4, 5), (2, 3, 4), (2, 3, 5), (2, 4, 5), (3, 4, 5), (3, 4, 6), (3, 4, 7), (3, 4, 8), (3, 4, 9), (3, 4, 10), (3, 4, 11), (3, 5, 6), (3, 5, 7), (3, 5, 8), (3, 5, 9), (3, 5, 10), (3, 5, 11), (3, 6, 7), (3, 6, 8), (3, 6, 9), (3, 6, 10), (3, 6, 11), (3, 7, 8), (3, 7, 9), (3, 7, 10), (3, 7, 11), (3, 8, 9), (3, 8, 10), (3, 8, 11), (3, 9, 10), (3, 9, 11), (3, 10, 11), (4, 5, 6), (4, 5, 7), (4, 5, 8), (4, 5, 9), (4, 5, 10), (4, 5, 11), (4, 6, 7), (4, 6, 8), (4, 6, 9), (4, 6, 10), (4, 6, 11), (4, 7, 8), (4, 7, 9), (4, 7, 10), (4, 7, 11), (4, 8, 9), (4, 8, 10), (4, 8, 11), (4, 9, 10), (4, 9, 11), (4, 10, 11), (5, 6, 7), (5, 6, 8), (5, 6, 9), (5, 6, 10), (5, 6, 11), (5, 7, 8), (5, 7, 9), (5, 7, 10), (5, 7, 11), (5, 8, 9), (5, 8, 10), (5, 8, 11), (5, 9, 10), (5, 9, 11), (5, 10, 11)]
2: 3 < 4 // possibilities: 24 [(0, 4, 5), (1, 4, 5), (2, 4, 5), (4, 5, 6), (4, 5, 7), (4, 5, 8), (4, 5, 9), (4, 5, 10), (4, 5, 11), (4, 6, 7), (4, 6, 8), (4, 6, 9), (4, 6, 10), (4, 6, 11), (4, 7, 8), (4, 7, 9), (4, 7, 10), (4, 7, 11), (4, 8, 9), (4, 8, 10), (4, 8, 11), (4, 9, 10), (4, 9, 11), (4, 10, 11)]
3: 0, 6, 7 < 1, 8, 9 // possibilities: 8 [(1, 4, 5), (4, 5, 8), (4, 5, 9), (4, 8, 9), (4, 8, 10), (4, 8, 11), (4, 9, 10), (4, 9, 11)]
4: 5 < 8 // possibilities: 3 [(4, 8, 9), (4, 8, 10), (4, 8, 11)]
5: 9 < 10 // result = (4, 8, 10)
5: 9 = 10 // result = (4, 8, 11)
5: 9 > 10 // result = (4, 8, 9)
4: 5 = 8 // possibilities: 3 [(4, 5, 8), (4, 9, 10), (4, 9, 11)]
5: 5 < 10 // result = (4, 9, 10)
5: 5 = 10 // result = (4, 9, 11)
5: 5 > 10 // result = (4, 5, 8)
4: 5 > 8 // possibilities: 2 [(1, 4, 5), (4, 5, 9)]
5: 0 < 1 // result = (1, 4, 5)
5: 0 = 1 // result = (4, 5, 9)
5: 0 > 1 // !!! impossible
3: 0, 6, 7 = 1, 8, 9 // possibilities: 8 [(2, 4, 5), (4, 5, 10), (4, 5, 11), (4, 6, 8), (4, 6, 9), (4, 7, 8), (4, 7, 9), (4, 10, 11)]
4: 5 < 6 // possibilities: 2 [(4, 6, 8), (4, 6, 9)]
5: 0 < 8 // result = (4, 6, 8)
5: 0 = 8 // result = (4, 6, 9)
5: 0 > 8 // !!! impossible
4: 5 = 6 // possibilities: 3 [(4, 7, 8), (4, 7, 9), (4, 10, 11)]
5: 8 < 9 // result = (4, 7, 9)
5: 8 = 9 // result = (4, 10, 11)
5: 8 > 9 // result = (4, 7, 8)
4: 5 > 6 // possibilities: 3 [(2, 4, 5), (4, 5, 10), (4, 5, 11)]
5: 2 < 10 // result = (4, 5, 10)
5: 2 = 10 // result = (4, 5, 11)
5: 2 > 10 // result = (2, 4, 5)
3: 0, 6, 7 > 1, 8, 9 // possibilities: 8 [(0, 4, 5), (4, 5, 6), (4, 5, 7), (4, 6, 7), (4, 6, 10), (4, 6, 11), (4, 7, 10), (4, 7, 11)]
4: 5 < 6 // possibilities: 3 [(4, 6, 7), (4, 6, 10), (4, 6, 11)]
5: 7 < 10 // result = (4, 6, 10)
5: 7 = 10 // result = (4, 6, 11)
5: 7 > 10 // result = (4, 6, 7)
4: 5 = 6 // possibilities: 3 [(4, 5, 6), (4, 7, 10), (4, 7, 11)]
5: 5 < 10 // result = (4, 7, 10)
5: 5 = 10 // result = (4, 7, 11)
5: 5 > 10 // result = (4, 5, 6)
4: 5 > 6 // possibilities: 2 [(0, 4, 5), (4, 5, 7)]
5: 0 < 1 // !!! impossible
5: 0 = 1 // result = (4, 5, 7)
5: 0 > 1 // result = (0, 4, 5)
2: 3 = 4 // possibilities: 25 [(0, 3, 4), (1, 3, 4), (2, 3, 4), (3, 4, 5), (3, 4, 6), (3, 4, 7), (3, 4, 8), (3, 4, 9), (3, 4, 10), (3, 4, 11), (5, 6, 7), (5, 6, 8), (5, 6, 9), (5, 6, 10), (5, 6, 11), (5, 7, 8), (5, 7, 9), (5, 7, 10), (5, 7, 11), (5, 8, 9), (5, 8, 10), (5, 8, 11), (5, 9, 10), (5, 9, 11), (5, 10, 11)]
3: 0, 3 < 6, 7 // possibilities: 9 [(5, 6, 7), (5, 6, 8), (5, 6, 9), (5, 6, 10), (5, 6, 11), (5, 7, 8), (5, 7, 9), (5, 7, 10), (5, 7, 11)]
4: 6, 8 < 7, 9 // possibilities: 3 [(5, 7, 9), (5, 7, 10), (5, 7, 11)]
5: 9 < 10 // result = (5, 7, 10)
5: 9 = 10 // result = (5, 7, 11)
5: 9 > 10 // result = (5, 7, 9)
4: 6, 8 = 7, 9 // possibilities: 3 [(5, 6, 7), (5, 6, 9), (5, 7, 8)]
5: 6 < 7 // result = (5, 7, 8)
5: 6 = 7 // result = (5, 6, 7)
5: 6 > 7 // result = (5, 6, 9)
4: 6, 8 > 7, 9 // possibilities: 3 [(5, 6, 8), (5, 6, 10), (5, 6, 11)]
5: 8 < 10 // result = (5, 6, 10)
5: 8 = 10 // result = (5, 6, 11)
5: 8 > 10 // result = (5, 6, 8)
3: 0, 3 = 6, 7 // possibilities: 8 [(3, 4, 6), (3, 4, 7), (5, 8, 9), (5, 8, 10), (5, 8, 11), (5, 9, 10), (5, 9, 11), (5, 10, 11)]
4: 3 < 8 // possibilities: 3 [(5, 8, 9), (5, 8, 10), (5, 8, 11)]
5: 9 < 10 // result = (5, 8, 10)
5: 9 = 10 // result = (5, 8, 11)
5: 9 > 10 // result = (5, 8, 9)
4: 3 = 8 // possibilities: 3 [(5, 9, 10), (5, 9, 11), (5, 10, 11)]
5: 9 < 10 // result = (5, 10, 11)
5: 9 = 10 // result = (5, 9, 10)
5: 9 > 10 // result = (5, 9, 11)
4: 3 > 8 // possibilities: 2 [(3, 4, 6), (3, 4, 7)]
5: 0 < 6 // result = (3, 4, 6)
5: 0 = 6 // result = (3, 4, 7)
5: 0 > 6 // !!! impossible
3: 0, 3 > 6, 7 // possibilities: 8 [(0, 3, 4), (1, 3, 4), (2, 3, 4), (3, 4, 5), (3, 4, 8), (3, 4, 9), (3, 4, 10), (3, 4, 11)]
4: 0, 1, 2 < 5, 6, 8 // possibilities: 2 [(3, 4, 5), (3, 4, 8)]
5: 0 < 5 // result = (3, 4, 5)
5: 0 = 5 // result = (3, 4, 8)
5: 0 > 5 // !!! impossible
4: 0, 1, 2 = 5, 6, 8 // possibilities: 3 [(3, 4, 9), (3, 4, 10), (3, 4, 11)]
5: 9 < 10 // result = (3, 4, 10)
5: 9 = 10 // result = (3, 4, 11)
5: 9 > 10 // result = (3, 4, 9)
4: 0, 1, 2 > 5, 6, 8 // possibilities: 3 [(0, 3, 4), (1, 3, 4), (2, 3, 4)]
5: 0 < 1 // result = (1, 3, 4)
5: 0 = 1 // result = (2, 3, 4)
5: 0 > 1 // result = (0, 3, 4)
2: 3 > 4 // possibilities: 24 [(0, 3, 5), (1, 3, 5), (2, 3, 5), (3, 5, 6), (3, 5, 7), (3, 5, 8), (3, 5, 9), (3, 5, 10), (3, 5, 11), (3, 6, 7), (3, 6, 8), (3, 6, 9), (3, 6, 10), (3, 6, 11), (3, 7, 8), (3, 7, 9), (3, 7, 10), (3, 7, 11), (3, 8, 9), (3, 8, 10), (3, 8, 11), (3, 9, 10), (3, 9, 11), (3, 10, 11)]
3: 0, 6, 7 < 1, 8, 9 // possibilities: 8 [(1, 3, 5), (3, 5, 8), (3, 5, 9), (3, 8, 9), (3, 8, 10), (3, 8, 11), (3, 9, 10), (3, 9, 11)]
4: 5 < 8 // possibilities: 3 [(3, 8, 9), (3, 8, 10), (3, 8, 11)]
5: 9 < 10 // result = (3, 8, 10)
5: 9 = 10 // result = (3, 8, 11)
5: 9 > 10 // result = (3, 8, 9)
4: 5 = 8 // possibilities: 3 [(3, 5, 8), (3, 9, 10), (3, 9, 11)]
5: 5 < 10 // result = (3, 9, 10)
5: 5 = 10 // result = (3, 9, 11)
5: 5 > 10 // result = (3, 5, 8)
4: 5 > 8 // possibilities: 2 [(1, 3, 5), (3, 5, 9)]
5: 0 < 1 // result = (1, 3, 5)
5: 0 = 1 // result = (3, 5, 9)
5: 0 > 1 // !!! impossible
3: 0, 6, 7 = 1, 8, 9 // possibilities: 8 [(2, 3, 5), (3, 5, 10), (3, 5, 11), (3, 6, 8), (3, 6, 9), (3, 7, 8), (3, 7, 9), (3, 10, 11)]
4: 5 < 6 // possibilities: 2 [(3, 6, 8), (3, 6, 9)]
5: 0 < 8 // result = (3, 6, 8)
5: 0 = 8 // result = (3, 6, 9)
5: 0 > 8 // !!! impossible
4: 5 = 6 // possibilities: 3 [(3, 7, 8), (3, 7, 9), (3, 10, 11)]
5: 8 < 9 // result = (3, 7, 9)
5: 8 = 9 // result = (3, 10, 11)
5: 8 > 9 // result = (3, 7, 8)
4: 5 > 6 // possibilities: 3 [(2, 3, 5), (3, 5, 10), (3, 5, 11)]
5: 2 < 10 // result = (3, 5, 10)
5: 2 = 10 // result = (3, 5, 11)
5: 2 > 10 // result = (2, 3, 5)
3: 0, 6, 7 > 1, 8, 9 // possibilities: 8 [(0, 3, 5), (3, 5, 6), (3, 5, 7), (3, 6, 7), (3, 6, 10), (3, 6, 11), (3, 7, 10), (3, 7, 11)]
4: 5 < 6 // possibilities: 3 [(3, 6, 7), (3, 6, 10), (3, 6, 11)]
5: 7 < 10 // result = (3, 6, 10)
5: 7 = 10 // result = (3, 6, 11)
5: 7 > 10 // result = (3, 6, 7)
4: 5 = 6 // possibilities: 3 [(3, 5, 6), (3, 7, 10), (3, 7, 11)]
5: 5 < 10 // result = (3, 7, 10)
5: 5 = 10 // result = (3, 7, 11)
5: 5 > 10 // result = (3, 5, 6)
4: 5 > 6 // possibilities: 2 [(0, 3, 5), (3, 5, 7)]
5: 0 < 1 // !!! impossible
5: 0 = 1 // result = (3, 5, 7)
5: 0 > 1 // result = (0, 3, 5)
1: 0, 1, 2 = 3, 4, 5 // possibilities: 74 [(0, 3, 6), (0, 3, 7), (0, 3, 8), (0, 3, 9), (0, 3, 10), (0, 3, 11), (0, 4, 6), (0, 4, 7), (0, 4, 8), (0, 4, 9), (0, 4, 10), (0, 4, 11), (0, 5, 6), (0, 5, 7), (0, 5, 8), (0, 5, 9), (0, 5, 10), (0, 5, 11), (1, 3, 6), (1, 3, 7), (1, 3, 8), (1, 3, 9), (1, 3, 10), (1, 3, 11), (1, 4, 6), (1, 4, 7), (1, 4, 8), (1, 4, 9), (1, 4, 10), (1, 4, 11), (1, 5, 6), (1, 5, 7), (1, 5, 8), (1, 5, 9), (1, 5, 10), (1, 5, 11), (2, 3, 6), (2, 3, 7), (2, 3, 8), (2, 3, 9), (2, 3, 10), (2, 3, 11), (2, 4, 6), (2, 4, 7), (2, 4, 8), (2, 4, 9), (2, 4, 10), (2, 4, 11), (2, 5, 6), (2, 5, 7), (2, 5, 8), (2, 5, 9), (2, 5, 10), (2, 5, 11), (6, 7, 8), (6, 7, 9), (6, 7, 10), (6, 7, 11), (6, 8, 9), (6, 8, 10), (6, 8, 11), (6, 9, 10), (6, 9, 11), (6, 10, 11), (7, 8, 9), (7, 8, 10), (7, 8, 11), (7, 9, 10), (7, 9, 11), (7, 10, 11), (8, 9, 10), (8, 9, 11), (8, 10, 11), (9, 10, 11)]
2: 0, 3, 6 < 1, 4, 7 // possibilities: 25 [(0, 4, 7), (1, 3, 7), (1, 4, 6), (1, 4, 7), (1, 4, 8), (1, 4, 9), (1, 4, 10), (1, 4, 11), (1, 5, 7), (1, 5, 8), (1, 5, 9), (1, 5, 10), (1, 5, 11), (2, 4, 7), (2, 4, 8), (2, 4, 9), (2, 4, 10), (2, 4, 11), (2, 5, 7), (7, 8, 9), (7, 8, 10), (7, 8, 11), (7, 9, 10), (7, 9, 11), (7, 10, 11)]
3: 1 < 7 // possibilities: 9 [(0, 4, 7), (2, 4, 7), (2, 5, 7), (7, 8, 9), (7, 8, 10), (7, 8, 11), (7, 9, 10), (7, 9, 11), (7, 10, 11)]
4: 0, 2 < 1, 8 // possibilities: 3 [(7, 8, 9), (7, 8, 10), (7, 8, 11)]
5: 9 < 10 // result = (7, 8, 10)
5: 9 = 10 // result = (7, 8, 11)
5: 9 > 10 // result = (7, 8, 9)
4: 0, 2 = 1, 8 // possibilities: 3 [(7, 9, 10), (7, 9, 11), (7, 10, 11)]
5: 9 < 10 // result = (7, 10, 11)
5: 9 = 10 // result = (7, 9, 10)
5: 9 > 10 // result = (7, 9, 11)
4: 0, 2 > 1, 8 // possibilities: 3 [(0, 4, 7), (2, 4, 7), (2, 5, 7)]
5: 0 < 5 // result = (2, 5, 7)
5: 0 = 5 // result = (2, 4, 7)
5: 0 > 5 // result = (0, 4, 7)
3: 1 = 7 // possibilities: 7 [(1, 3, 7), (1, 4, 7), (1, 5, 7), (2, 4, 8), (2, 4, 9), (2, 4, 10), (2, 4, 11)]
4: 1 < 8 // result = (2, 4, 8)
4: 1 = 8 // possibilities: 3 [(2, 4, 9), (2, 4, 10), (2, 4, 11)]
5: 9 < 10 // result = (2, 4, 10)
5: 9 = 10 // result = (2, 4, 11)
5: 9 > 10 // result = (2, 4, 9)
4: 1 > 8 // possibilities: 3 [(1, 3, 7), (1, 4, 7), (1, 5, 7)]
5: 3 < 4 // result = (1, 4, 7)
5: 3 = 4 // result = (1, 5, 7)
5: 3 > 4 // result = (1, 3, 7)
3: 1 > 7 // possibilities: 9 [(1, 4, 6), (1, 4, 8), (1, 4, 9), (1, 4, 10), (1, 4, 11), (1, 5, 8), (1, 5, 9), (1, 5, 10), (1, 5, 11)]
4: 0, 4, 8 < 5, 6, 9 // possibilities: 3 [(1, 5, 9), (1, 5, 10), (1, 5, 11)]
5: 9 < 10 // result = (1, 5, 10)
5: 9 = 10 // result = (1, 5, 11)
5: 9 > 10 // result = (1, 5, 9)
4: 0, 4, 8 = 5, 6, 9 // possibilities: 3 [(1, 4, 6), (1, 4, 9), (1, 5, 8)]
5: 5 < 6 // result = (1, 4, 6)
5: 5 = 6 // result = (1, 4, 9)
5: 5 > 6 // result = (1, 5, 8)
4: 0, 4, 8 > 5, 6, 9 // possibilities: 3 [(1, 4, 8), (1, 4, 10), (1, 4, 11)]
5: 8 < 10 // result = (1, 4, 10)
5: 8 = 10 // result = (1, 4, 11)
5: 8 > 10 // result = (1, 4, 8)
2: 0, 3, 6 = 1, 4, 7 // possibilities: 24 [(0, 4, 8), (0, 4, 9), (0, 4, 10), (0, 4, 11), (0, 5, 7), (1, 3, 8), (1, 3, 9), (1, 3, 10), (1, 3, 11), (1, 5, 6), (2, 3, 7), (2, 4, 6), (2, 5, 8), (2, 5, 9), (2, 5, 10), (2, 5, 11), (6, 7, 8), (6, 7, 9), (6, 7, 10), (6, 7, 11), (8, 9, 10), (8, 9, 11), (8, 10, 11), (9, 10, 11)]
3: 0, 2 < 3, 8 // possibilities: 8 [(1, 3, 8), (1, 3, 9), (1, 3, 10), (1, 3, 11), (6, 7, 8), (8, 9, 10), (8, 9, 11), (8, 10, 11)]
4: 1 < 9 // possibilities: 2 [(8, 9, 10), (8, 9, 11)]
5: 0 < 10 // result = (8, 9, 10)
5: 0 = 10 // result = (8, 9, 11)
5: 0 > 10 // !!! impossible
4: 1 = 9 // possibilities: 3 [(1, 3, 9), (6, 7, 8), (8, 10, 11)]
5: 1 < 6 // result = (6, 7, 8)
5: 1 = 6 // result = (8, 10, 11)
5: 1 > 6 // result = (1, 3, 9)
4: 1 > 9 // possibilities: 3 [(1, 3, 8), (1, 3, 10), (1, 3, 11)]
5: 8 < 10 // result = (1, 3, 10)
5: 8 = 10 // result = (1, 3, 11)
5: 8 > 10 // result = (1, 3, 8)
3: 0, 2 = 3, 8 // possibilities: 8 [(0, 4, 8), (1, 5, 6), (2, 3, 7), (2, 5, 8), (6, 7, 9), (6, 7, 10), (6, 7, 11), (9, 10, 11)]
4: 0, 1 < 3, 9 // possibilities: 3 [(2, 3, 7), (6, 7, 9), (9, 10, 11)]
5: 2 < 6 // result = (6, 7, 9)
5: 2 = 6 // result = (9, 10, 11)
5: 2 > 6 // result = (2, 3, 7)
4: 0, 1 = 3, 9 // possibilities: 3 [(2, 5, 8), (6, 7, 10), (6, 7, 11)]
5: 2 < 10 // result = (6, 7, 10)
5: 2 = 10 // result = (6, 7, 11)
5: 2 > 10 // result = (2, 5, 8)
4: 0, 1 > 3, 9 // possibilities: 2 [(0, 4, 8), (1, 5, 6)]
5: 0 < 1 // result = (1, 5, 6)
5: 0 = 1 // !!! impossible
5: 0 > 1 // result = (0, 4, 8)
3: 0, 2 > 3, 8 // possibilities: 8 [(0, 4, 9), (0, 4, 10), (0, 4, 11), (0, 5, 7), (2, 4, 6), (2, 5, 9), (2, 5, 10), (2, 5, 11)]
4: 0 < 5 // possibilities: 3 [(2, 5, 9), (2, 5, 10), (2, 5, 11)]
5: 9 < 10 // result = (2, 5, 10)
5: 9 = 10 // result = (2, 5, 11)
5: 9 > 10 // result = (2, 5, 9)
4: 0 = 5 // possibilities: 2 [(0, 5, 7), (2, 4, 6)]
5: 0 < 1 // !!! impossible
5: 0 = 1 // result = (2, 4, 6)
5: 0 > 1 // result = (0, 5, 7)
4: 0 > 5 // possibilities: 3 [(0, 4, 9), (0, 4, 10), (0, 4, 11)]
5: 9 < 10 // result = (0, 4, 10)
5: 9 = 10 // result = (0, 4, 11)
5: 9 > 10 // result = (0, 4, 9)
2: 0, 3, 6 > 1, 4, 7 // possibilities: 25 [(0, 3, 6), (0, 3, 7), (0, 3, 8), (0, 3, 9), (0, 3, 10), (0, 3, 11), (0, 4, 6), (0, 5, 6), (0, 5, 8), (0, 5, 9), (0, 5, 10), (0, 5, 11), (1, 3, 6), (2, 3, 6), (2, 3, 8), (2, 3, 9), (2, 3, 10), (2, 3, 11), (2, 5, 6), (6, 8, 9), (6, 8, 10), (6, 8, 11), (6, 9, 10), (6, 9, 11), (6, 10, 11)]
3: 0 < 6 // possibilities: 9 [(1, 3, 6), (2, 3, 6), (2, 5, 6), (6, 8, 9), (6, 8, 10), (6, 8, 11), (6, 9, 10), (6, 9, 11), (6, 10, 11)]
4: 0, 8 < 1, 2 // possibilities: 3 [(1, 3, 6), (2, 3, 6), (2, 5, 6)]
5: 1 < 5 // result = (2, 5, 6)
5: 1 = 5 // result = (2, 3, 6)
5: 1 > 5 // result = (1, 3, 6)
4: 0, 8 = 1, 2 // possibilities: 3 [(6, 9, 10), (6, 9, 11), (6, 10, 11)]
5: 9 < 10 // result = (6, 10, 11)
5: 9 = 10 // result = (6, 9, 10)
5: 9 > 10 // result = (6, 9, 11)
4: 0, 8 > 1, 2 // possibilities: 3 [(6, 8, 9), (6, 8, 10), (6, 8, 11)]
5: 9 < 10 // result = (6, 8, 10)
5: 9 = 10 // result = (6, 8, 11)
5: 9 > 10 // result = (6, 8, 9)
3: 0 = 6 // possibilities: 7 [(0, 3, 6), (0, 4, 6), (0, 5, 6), (2, 3, 8), (2, 3, 9), (2, 3, 10), (2, 3, 11)]
4: 0 < 8 // result = (2, 3, 8)
4: 0 = 8 // possibilities: 3 [(2, 3, 9), (2, 3, 10), (2, 3, 11)]
5: 9 < 10 // result = (2, 3, 10)
5: 9 = 10 // result = (2, 3, 11)
5: 9 > 10 // result = (2, 3, 9)
4: 0 > 8 // possibilities: 3 [(0, 3, 6), (0, 4, 6), (0, 5, 6)]
5: 3 < 4 // result = (0, 4, 6)
5: 3 = 4 // result = (0, 5, 6)
5: 3 > 4 // result = (0, 3, 6)
3: 0 > 6 // possibilities: 9 [(0, 3, 7), (0, 3, 8), (0, 3, 9), (0, 3, 10), (0, 3, 11), (0, 5, 8), (0, 5, 9), (0, 5, 10), (0, 5, 11)]
4: 1, 3, 8 < 5, 7, 9 // possibilities: 3 [(0, 5, 9), (0, 5, 10), (0, 5, 11)]
5: 9 < 10 // result = (0, 5, 10)
5: 9 = 10 // result = (0, 5, 11)
5: 9 > 10 // result = (0, 5, 9)
4: 1, 3, 8 = 5, 7, 9 // possibilities: 3 [(0, 3, 7), (0, 3, 9), (0, 5, 8)]
5: 5 < 7 // result = (0, 3, 7)
5: 5 = 7 // result = (0, 3, 9)
5: 5 > 7 // result = (0, 5, 8)
4: 1, 3, 8 > 5, 7, 9 // possibilities: 3 [(0, 3, 8), (0, 3, 10), (0, 3, 11)]
5: 8 < 10 // result = (0, 3, 10)
5: 8 = 10 // result = (0, 3, 11)
5: 8 > 10 // result = (0, 3, 8)
1: 0, 1, 2 > 3, 4, 5 // possibilities: 73 [(0, 1, 2), (0, 1, 3), (0, 1, 4), (0, 1, 5), (0, 1, 6), (0, 1, 7), (0, 1, 8), (0, 1, 9), (0, 1, 10), (0, 1, 11), (0, 2, 3), (0, 2, 4), (0, 2, 5), (0, 2, 6), (0, 2, 7), (0, 2, 8), (0, 2, 9), (0, 2, 10), (0, 2, 11), (0, 6, 7), (0, 6, 8), (0, 6, 9), (0, 6, 10), (0, 6, 11), (0, 7, 8), (0, 7, 9), (0, 7, 10), (0, 7, 11), (0, 8, 9), (0, 8, 10), (0, 8, 11), (0, 9, 10), (0, 9, 11), (0, 10, 11), (1, 2, 3), (1, 2, 4), (1, 2, 5), (1, 2, 6), (1, 2, 7), (1, 2, 8), (1, 2, 9), (1, 2, 10), (1, 2, 11), (1, 6, 7), (1, 6, 8), (1, 6, 9), (1, 6, 10), (1, 6, 11), (1, 7, 8), (1, 7, 9), (1, 7, 10), (1, 7, 11), (1, 8, 9), (1, 8, 10), (1, 8, 11), (1, 9, 10), (1, 9, 11), (1, 10, 11), (2, 6, 7), (2, 6, 8), (2, 6, 9), (2, 6, 10), (2, 6, 11), (2, 7, 8), (2, 7, 9), (2, 7, 10), (2, 7, 11), (2, 8, 9), (2, 8, 10), (2, 8, 11), (2, 9, 10), (2, 9, 11), (2, 10, 11)]
2: 0 < 1 // possibilities: 24 [(1, 2, 3), (1, 2, 4), (1, 2, 5), (1, 2, 6), (1, 2, 7), (1, 2, 8), (1, 2, 9), (1, 2, 10), (1, 2, 11), (1, 6, 7), (1, 6, 8), (1, 6, 9), (1, 6, 10), (1, 6, 11), (1, 7, 8), (1, 7, 9), (1, 7, 10), (1, 7, 11), (1, 8, 9), (1, 8, 10), (1, 8, 11), (1, 9, 10), (1, 9, 11), (1, 10, 11)]
3: 3, 6, 7 < 4, 8, 9 // possibilities: 8 [(1, 2, 4), (1, 2, 8), (1, 2, 9), (1, 8, 9), (1, 8, 10), (1, 8, 11), (1, 9, 10), (1, 9, 11)]
4: 2 < 8 // possibilities: 3 [(1, 8, 9), (1, 8, 10), (1, 8, 11)]
5: 9 < 10 // result = (1, 8, 10)
5: 9 = 10 // result = (1, 8, 11)
5: 9 > 10 // result = (1, 8, 9)
4: 2 = 8 // possibilities: 3 [(1, 2, 8), (1, 9, 10), (1, 9, 11)]
5: 2 < 10 // result = (1, 9, 10)
5: 2 = 10 // result = (1, 9, 11)
5: 2 > 10 // result = (1, 2, 8)
4: 2 > 8 // possibilities: 2 [(1, 2, 4), (1, 2, 9)]
5: 0 < 4 // result = (1, 2, 4)
5: 0 = 4 // result = (1, 2, 9)
5: 0 > 4 // !!! impossible
3: 3, 6, 7 = 4, 8, 9 // possibilities: 8 [(1, 2, 5), (1, 2, 10), (1, 2, 11), (1, 6, 8), (1, 6, 9), (1, 7, 8), (1, 7, 9), (1, 10, 11)]
4: 2 < 6 // possibilities: 2 [(1, 6, 8), (1, 6, 9)]
5: 0 < 8 // result = (1, 6, 8)
5: 0 = 8 // result = (1, 6, 9)
5: 0 > 8 // !!! impossible
4: 2 = 6 // possibilities: 3 [(1, 7, 8), (1, 7, 9), (1, 10, 11)]
5: 8 < 9 // result = (1, 7, 9)
5: 8 = 9 // result = (1, 10, 11)
5: 8 > 9 // result = (1, 7, 8)
4: 2 > 6 // possibilities: 3 [(1, 2, 5), (1, 2, 10), (1, 2, 11)]
5: 5 < 10 // result = (1, 2, 10)
5: 5 = 10 // result = (1, 2, 11)
5: 5 > 10 // result = (1, 2, 5)
3: 3, 6, 7 > 4, 8, 9 // possibilities: 8 [(1, 2, 3), (1, 2, 6), (1, 2, 7), (1, 6, 7), (1, 6, 10), (1, 6, 11), (1, 7, 10), (1, 7, 11)]
4: 2 < 6 // possibilities: 3 [(1, 6, 7), (1, 6, 10), (1, 6, 11)]
5: 7 < 10 // result = (1, 6, 10)
5: 7 = 10 // result = (1, 6, 11)
5: 7 > 10 // result = (1, 6, 7)
4: 2 = 6 // possibilities: 3 [(1, 2, 6), (1, 7, 10), (1, 7, 11)]
5: 2 < 10 // result = (1, 7, 10)
5: 2 = 10 // result = (1, 7, 11)
5: 2 > 10 // result = (1, 2, 6)
4: 2 > 6 // possibilities: 2 [(1, 2, 3), (1, 2, 7)]
5: 0 < 3 // result = (1, 2, 3)
5: 0 = 3 // result = (1, 2, 7)
5: 0 > 3 // !!! impossible
2: 0 = 1 // possibilities: 25 [(0, 1, 2), (0, 1, 3), (0, 1, 4), (0, 1, 5), (0, 1, 6), (0, 1, 7), (0, 1, 8), (0, 1, 9), (0, 1, 10), (0, 1, 11), (2, 6, 7), (2, 6, 8), (2, 6, 9), (2, 6, 10), (2, 6, 11), (2, 7, 8), (2, 7, 9), (2, 7, 10), (2, 7, 11), (2, 8, 9), (2, 8, 10), (2, 8, 11), (2, 9, 10), (2, 9, 11), (2, 10, 11)]
3: 0, 3 < 6, 7 // possibilities: 9 [(2, 6, 7), (2, 6, 8), (2, 6, 9), (2, 6, 10), (2, 6, 11), (2, 7, 8), (2, 7, 9), (2, 7, 10), (2, 7, 11)]
4: 6, 8 < 7, 9 // possibilities: 3 [(2, 7, 9), (2, 7, 10), (2, 7, 11)]
5: 9 < 10 // result = (2, 7, 10)
5: 9 = 10 // result = (2, 7, 11)
5: 9 > 10 // result = (2, 7, 9)
4: 6, 8 = 7, 9 // possibilities: 3 [(2, 6, 7), (2, 6, 9), (2, 7, 8)]
5: 6 < 7 // result = (2, 7, 8)
5: 6 = 7 // result = (2, 6, 7)
5: 6 > 7 // result = (2, 6, 9)
4: 6, 8 > 7, 9 // possibilities: 3 [(2, 6, 8), (2, 6, 10), (2, 6, 11)]
5: 8 < 10 // result = (2, 6, 10)
5: 8 = 10 // result = (2, 6, 11)
5: 8 > 10 // result = (2, 6, 8)
3: 0, 3 = 6, 7 // possibilities: 8 [(0, 1, 6), (0, 1, 7), (2, 8, 9), (2, 8, 10), (2, 8, 11), (2, 9, 10), (2, 9, 11), (2, 10, 11)]
4: 0 < 8 // possibilities: 3 [(2, 8, 9), (2, 8, 10), (2, 8, 11)]
5: 9 < 10 // result = (2, 8, 10)
5: 9 = 10 // result = (2, 8, 11)
5: 9 > 10 // result = (2, 8, 9)
4: 0 = 8 // possibilities: 3 [(2, 9, 10), (2, 9, 11), (2, 10, 11)]
5: 9 < 10 // result = (2, 10, 11)
5: 9 = 10 // result = (2, 9, 10)
5: 9 > 10 // result = (2, 9, 11)
4: 0 > 8 // possibilities: 2 [(0, 1, 6), (0, 1, 7)]
5: 0 < 6 // !!! impossible
5: 0 = 6 // result = (0, 1, 6)
5: 0 > 6 // result = (0, 1, 7)
3: 0, 3 > 6, 7 // possibilities: 8 [(0, 1, 2), (0, 1, 3), (0, 1, 4), (0, 1, 5), (0, 1, 8), (0, 1, 9), (0, 1, 10), (0, 1, 11)]
4: 2, 3, 4 < 5, 6, 8 // possibilities: 2 [(0, 1, 5), (0, 1, 8)]
5: 0 < 5 // !!! impossible
5: 0 = 5 // result = (0, 1, 5)
5: 0 > 5 // result = (0, 1, 8)
4: 2, 3, 4 = 5, 6, 8 // possibilities: 3 [(0, 1, 9), (0, 1, 10), (0, 1, 11)]
5: 9 < 10 // result = (0, 1, 10)
5: 9 = 10 // result = (0, 1, 11)
5: 9 > 10 // result = (0, 1, 9)
4: 2, 3, 4 > 5, 6, 8 // possibilities: 3 [(0, 1, 2), (0, 1, 3), (0, 1, 4)]
5: 2 < 3 // result = (0, 1, 3)
5: 2 = 3 // result = (0, 1, 4)
5: 2 > 3 // result = (0, 1, 2)
2: 0 > 1 // possibilities: 24 [(0, 2, 3), (0, 2, 4), (0, 2, 5), (0, 2, 6), (0, 2, 7), (0, 2, 8), (0, 2, 9), (0, 2, 10), (0, 2, 11), (0, 6, 7), (0, 6, 8), (0, 6, 9), (0, 6, 10), (0, 6, 11), (0, 7, 8), (0, 7, 9), (0, 7, 10), (0, 7, 11), (0, 8, 9), (0, 8, 10), (0, 8, 11), (0, 9, 10), (0, 9, 11), (0, 10, 11)]
3: 3, 6, 7 < 4, 8, 9 // possibilities: 8 [(0, 2, 4), (0, 2, 8), (0, 2, 9), (0, 8, 9), (0, 8, 10), (0, 8, 11), (0, 9, 10), (0, 9, 11)]
4: 2 < 8 // possibilities: 3 [(0, 8, 9), (0, 8, 10), (0, 8, 11)]
5: 9 < 10 // result = (0, 8, 10)
5: 9 = 10 // result = (0, 8, 11)
5: 9 > 10 // result = (0, 8, 9)
4: 2 = 8 // possibilities: 3 [(0, 2, 8), (0, 9, 10), (0, 9, 11)]
5: 2 < 10 // result = (0, 9, 10)
5: 2 = 10 // result = (0, 9, 11)
5: 2 > 10 // result = (0, 2, 8)
4: 2 > 8 // possibilities: 2 [(0, 2, 4), (0, 2, 9)]
5: 0 < 4 // !!! impossible
5: 0 = 4 // result = (0, 2, 4)
5: 0 > 4 // result = (0, 2, 9)
3: 3, 6, 7 = 4, 8, 9 // possibilities: 8 [(0, 2, 5), (0, 2, 10), (0, 2, 11), (0, 6, 8), (0, 6, 9), (0, 7, 8), (0, 7, 9), (0, 10, 11)]
4: 2 < 6 // possibilities: 2 [(0, 6, 8), (0, 6, 9)]
5: 0 < 8 // !!! impossible
5: 0 = 8 // result = (0, 6, 8)
5: 0 > 8 // result = (0, 6, 9)
4: 2 = 6 // possibilities: 3 [(0, 7, 8), (0, 7, 9), (0, 10, 11)]
5: 8 < 9 // result = (0, 7, 9)
5: 8 = 9 // result = (0, 10, 11)
5: 8 > 9 // result = (0, 7, 8)
4: 2 > 6 // possibilities: 3 [(0, 2, 5), (0, 2, 10), (0, 2, 11)]
5: 5 < 10 // result = (0, 2, 10)
5: 5 = 10 // result = (0, 2, 11)
5: 5 > 10 // result = (0, 2, 5)
3: 3, 6, 7 > 4, 8, 9 // possibilities: 8 [(0, 2, 3), (0, 2, 6), (0, 2, 7), (0, 6, 7), (0, 6, 10), (0, 6, 11), (0, 7, 10), (0, 7, 11)]
4: 2 < 6 // possibilities: 3 [(0, 6, 7), (0, 6, 10), (0, 6, 11)]
5: 7 < 10 // result = (0, 6, 10)
5: 7 = 10 // result = (0, 6, 11)
5: 7 > 10 // result = (0, 6, 7)
4: 2 = 6 // possibilities: 3 [(0, 2, 6), (0, 7, 10), (0, 7, 11)]
5: 2 < 10 // result = (0, 7, 10)
5: 2 = 10 // result = (0, 7, 11)
5: 2 > 10 // result = (0, 2, 6)
4: 2 > 6 // possibilities: 2 [(0, 2, 3), (0, 2, 7)]
5: 0 < 3 // !!! impossible
5: 0 = 3 // result = (0, 2, 3)
5: 0 > 3 // result = (0, 2, 7)

мен ме съмняваше именно това,
4е с 3,96 хода може защото винаги получаваш максимална информация от измерването.
Обаче топчетата все пак са цели и предполагах че за да има решение се налага да могат да се разделят на третинки и така да се слагат на кантара :)))

Какво ще кажеш за 22 топчета и 5 измервания - теоретично е възможно
имаме 4,95 измервания.
На практика обаче когато опитвах програмно - винаги ми оставаха за поседен вариант 2,1,0 като възможности, а не 1,1,1 за да ги определя в едно измерване! Все пак програмата ми не бе на пълно изброяване и кой знае - може и да има решение :))

пс: понеже си теоретик - имаш ли идея по темата ми
"За козлите малко по сериозно", която в момента стои на 5-6 място в списъка ... никой нищо не казва по нея

Съдържаниет е скрито
Влезте за да го видите

5 от 22. Пуснах го и няма проблем с 5 хода.
Output-а обаче е около 26K и ще се въздържа да го поствам.
Ако много държиш да го видиш, ще го дам.

Ако искаш да се тестваш, пробвай да отделиш 4 по-тежки топки от 13.
715 комбинации, F=5.98... Доста по-сериозно е от 2/22.
Става със 6 хода, пробвах.

За козлите - погледнах темата, но ми се препълни стека от препратки.
Ще чакам по-евтини времена, за да я погледна по-сериозно.

Айде весели празници!

shto da ne stava s 2x6. merim taka /maham sluchaite, kogato vednaga se okazva, che ot ednata strana sa po-tejkite, ami dopuskam, che ot samoto nachalo sa ot dvete strani/:

nachi 1-6 s/u 7-12 <- ravenstvo
1-3 s/u 4-6 <- vzimame po-tejkata strana, primerno 1-3
syshtoto za 7-9 s/u 10-12 primerno 10-12 e po-tejko

vadim topche ot 1-3 i merim drugite dve, ako sa ravni nachi vzetoto e tejkoto, ako ne, nachi po-tejkoto ot dvete e tejkoto...:P
syshtoto i za 10-12... 5 merenia minimum pri maximalno loshia sluchai za nas...

ako ot nachalo se okaje, che 2 ot topchetata sa v ednata strana, mereniata namaliavat, do 3 dori...

направил си значи програмка която вади решение?
абе наличието на излишък от информация би трябвало да обособи невъзможни резултати от определено замерване. има ли такива наистина в листинга с решението? но това което се чудя е ако излишика е толкова малък че да не стига дори за една забрана за определен резултат при измерване, то къде отива излишната информация...

Да, написах програмка. Невъзможни резултати има, можеш да ги видиш в листингите от предишните ми постинги (impossible).

Излишъкът се “крие” в неравномерното разделяне на все още възможните комбинации. С две думи – ето къде се обърквате (ти и safin) Ако все още възможните комбинации са N, то най-информативното теглене е това, резултатите от което ги разделят на 3 равни части (оттам и логаритъма във формулата). Ако N не се дели на 3 – ето ти излишък. Единствения случай, в който комбинациите са точна, по-голяма от 0 степен на 3 е когато отделяш 2 топки от 3. Така че рано или късно стигаме до брой възможни комбинации, неделящ се на 3 и вкарваме излишък.