Brain teaser for the week 20201031 每周烧次脑
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Difficulty level: ✮ ✮ ✮ ✮ ✮
Name three words that end in “DOUS.” 本期题目比较简单，请写出3个以dous结尾的词语。
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答案下期公布
By the New Year's Day, top 3 players
will get a gift from us!
元旦前，年度前三高手将获得神秘礼物！
Answer to the last week 上期答案 Brain teaser for the week 20201024 每周烧次脑
(c) 3 vs. 3
Label the 9 coins a, b, c, d, e, f, g, h, i. First weigh abc with ghi. If they balance, then heavy coin is either d, e, or f. So weigh d with e. If they balance, then the heavy coin is f. If they don’t balance, then whichever coin tips the scale is the heavy one. Suppose abc and ghi do not balance. Then whichever side tips the scale has the heavier coin. Suppose in this case the side with ghi has the heavy coin. Then, in the procedure done before, weigh g with h. If they balance, then i is heavy. If they don’t balance, then the coin that tips the scale downward is heavy.
Here is a more sophisticated solution:
Number the coins 1 through 9. In the first weighing, place coins 1, 2, and 3 on the left side of the scale, and place 4, 5, and 6 on the right side. Leave 7, 8 and 9 on the side. For the second weighing, regardless of the results of the first, place coins 1, 4, and 7 on the left, and place 2, 5, and 8 on the right. The following chart demonstrates how to determine which is the heaviest coin depending on these results. In this chart, the results displayed list which side of the balance scale was heavier.
Heavy | Results of First | Results of Second | ||||||||
Coin | Weighing | Weighing | ||||||||
1, 2, 3, vs. 4, 5, 6 | 1, 4, 7, vs. 2, 5, 8 | |||||||||
1 | Left | Left | ||||||||
2 | Left | Right | ||||||||
3 | Left | Equal | ||||||||
4 | Right | Left | ||||||||
5 | Right | Right | ||||||||
6 | Right | Equal | ||||||||
7 | Equal | Left | ||||||||
8 | Equal | Right | ||||||||
9 | Equal | Equal | ||||||||
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