There are 9 identical gold coins in a box but one of them is lighter than the others.Can you use a balance and weights only twice to find out which is thhe lighter one?
- abaformLv 51 十年前最愛解答
Divide the 9 gold coins into 3 slots, say A, B and C
First, compare the weights of A and B. There can be 3 cases:
i) weight(A) < weight(B). Let the 3 coins in A be a1, a2, a3
Here do the second step, compare a1 and a2. If weight(a1) =/= weight(a2), then the answer is obvious, otherwise a3 is lighter.
ii) weight(A) = weight(B). Let the 3 coins in C be c1, c2, c3
Perform the test like i) on c1 and c2 and get the result.
iii) weight(A) > weight(B). Let the 3 coins in B be b1, b2, b3
Perform the test like i) on b1 and b2 and get the result.