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(11/06) Griff Aloni : start with weighing out 3 shurikens. 3 beacuse if 1 of them is the fake you will know because they are a different mass compared to the other 2 which leads you to findind the weight of the real shurikens. After knowing the weight of the real ones. weigh out each of the remaining shurikens until you find 1 that is not consistant with the previous ones weighed. booyaaa
Shika: I said balancing scales, not weighing scale. Think Libra.
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(11/06) Char Siew Pao : Well, you wants to have it in 4 steps right?I dun know what do you mean by four steps but here is my solution. Since there are 20 shurikens and 19 are real but 1 is fake and the fake one is either heavier or lighter.
I will first divide them into sets of 4 shurikens. Thus 20 = 5 X 4 and I have 5 sets. Then I will compare them with the balance. Example: set 1 with set 2, set 1 with set 3, etc. After comparision, there will defiinitely be one which is heavier or lighter than the rest of the sets. This particular set thus contains the fake shuriken. I take note whether it is heavier or lighter than the rest of the sets as this is the clue to whether the fake shuriken is heavier or lighter. I have 4 shurikens left right?
I divide them again into sets of 2. 4 = 2 X 2 . I have 2 sets. Since from the previous weighting, I will know whether the fake shuriken is heavier or lighter. This time comparing the 2 sets, there will definitely be one set which is heavier or lighter. My fake shuriken is in that set.
Left 2 shurikens. Simple. Weight them again and then I will know the truth. Since I know whether the fake one is heavier or lighter. Thats all.
Shika: By 4 moves we mean that one is only allow to place shurikens on the balance 4 times. So try again.
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(12/06) Goroshi : 1. balance the 20 shurikens halved 10 and 10.. (the lighter side of
the balancing scale contains the fake ones)
2. balance the 10 shurikens with a fake one, halved 5 and 5.
3. balance the 5 shurikens with a fake one plus one shuriken from the original ones (so it would be even)making it 6, halved 3 and 3.
4. balance the 3 shurikens with a fake one plus one shuriken from the original ones (so it would be even)making it 4, halved 2 and 2.
get the lighter side.. and u got 1 fake and 1 original..
Shika: Wrong. I never said the fake shuriken is lighter than the real ones. That's what you have to establish within the 4 steps too.
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