Yatsu 發問於 科學及數學數學 · 1 十年前

f.1 maths

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?

1 個解答

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  • 1 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.

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