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2 < log_3(12) < 3, so at least 3 steps
- afazulzyanov August 10, 2015btw, log_3(24) < 3, and we are able to find if the odd marble is heavier or lighter
1:
(1, 2, 3, 4) < (5, 6, 7, 8) => x in (1, 2, 3, 4) and lighter or x in (5, 6, 7, 8) and heavier
1.1:
(1, 2, 3, 5) < (4, 10, 11, 12) => x in (1, 2, 3) and lighter
1.1.1:
1 < 2 => 1 is odd marble and lighter
1.1.2:
1 > 2 => 2 is odd marble and lighter
1.1.3:
1 = 2 => 3 is odd marble and lighter
1.2:
(1, 2, 3, 5) > (4, 10, 11, 12) => x is 4 and lighter or x is 5 and heavier
1.2.1:
1 > 4 => 4 is odd and lighter
1.2.2:
1 = 4 => 5 is odd asd heavier
1.3:
(1, 2, 3, 5) = (4, 10, 11, 12) => x in (6, 7, 8) and heavier
1.3.1:
6 < 7 => 7 is odd and heavier
1.3.2:
6 > 7 => 6 is odd and heavier
1.3.3:
6 = 7 => 8 is odd and heavier
2:
(1, 2, 3, 4) > (5, 6, 7, 8) is simular as 1
3:
(1, 2, 3, 4) = (5, 6, 7, 8)
3.1:
(9, 10, 11) > (1, 2, 3) => x in (9, 10, 11) and heavier
3.1.1:
9 > 10 => 9 is odd and heavier
3.1.2:
9 < 10 => 10 is odd and heavier
3.1.3:
9 = 10 => 11 is odd and heavier
3.2:
(9, 10, 11) < (1, 2, 3) => x in (1, 2, 3) and lighter
3.2.1:
9 > 10 => 10 is odd and lighter
3.2.2:
9 < 10 => 9 is odd and lighter
3.2.3:
9 = 10 => 11 is odd and lighter
3.3:
(9, 10, 11) = (1, 2, 3) => 12 is odd
3.3.1:
12 < 1 => 12 is odd and lighter
3.3.2:
12 > 1 => 12 is odd and heavier