標題:
A difficult maths question
發問:
There are 9 identical gold coins in a box but one of them is lighter than others. Can you use a balance and weights only twice to find out which is the lighter one?
最佳解答:
- 若m,n是正整數,p,q是實數不等於0且ax^(2m)+b(x^m)(y^n)+cy^(2n)被px^m+qy^n整除,試證aq^2+cp^2=bpq-
- 聯立二元一次方程～急！！@1@
- clamp的《X》@1@
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You can divide the 9 gold coins in 3 groups (Group A, B & C), 3 in each group. 1st Round: Put the 3 coins of Group A on the left side and 3 coins of Group B on the right side of the balance. If they are in balancing position, the one lighter would be in Group C. 2nd Round: Then, put 2 coins of Group C on the balance. If they are in balancing position, the lighter one would be the remaining one. Otherwise, you can find which one is lighter from the balance. If it is found in 1st Round that either Group A or Group B is lighter, you can just do the 2nd Round checking from the lighter Group as mentioned above and find which coin is lighter.
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