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香港三國論壇 > 天水城 > 推理遊戲2 - 新加坡高中數學競賽考題

發表者: Pearltea Aug 25 2015, 01:33

幾個月前一題高中數學競賽考題被電視主播放上FB, 引起了很大的爭論. 很多人不同意答案 (其實是有些爭議性). 大家試試算出&解釋, 然後再討論吧.

English (official version)

Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates:
May 15, 16, 19
June 17, 18
July 14, 16
August 14, 15, 17

Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.

Albert: I don't know when Cheryl's birthday is, but I know that Bernard doesn't know too.
Bernard: At first I don't know when Cheryl's birthday is, but I know now.
Albert: Then I also know when Cheryl's birthday is.

So when is Cheryl's birthday?
---------------------------------------

艾柏特和柏納剛認識雪莉，想要知道雪莉的生日，雪莉列出了十個可能的日期：
5月15日、5月16日、5月19日、6月17日
6月18日、7月14日、7月16日、8月14日
8月15日、8月17日

接著雪莉分別告訴艾柏特及柏納她生日的月及日，以下是艾柏特和柏納的回應。

艾柏特：我不知道雪莉的生日是哪一天，但我知道柏納也不知道
柏納：一開始我不知道雪莉的生日，但現在我知道了
艾柏特：那我也知道雪莉的生日了

請問雪莉的生日是那一天？

已經知道答案的板友請暫時不要回覆. 待提供答案後才一起討論

發表者: Caesar Aug 25 2015, 02:16

上原圖一下，之前玩過了，這裡就不玩了。

The answer itself isn't really important ,
In fact I believe many ppl r able to tell the answer ,
the difficulty in clearly explain how u achieve ur answer is the thing.

If I come up with this on an exam paper, it takes me both language and logic skill to score it
Probably can't fully score it even tho I know da answer

發表者: Pearltea Aug 25 2015, 02:28

QUOTE (Caesar @ Aug 25 2015, 10:16 )

I agree - but even on the language's side, it's highly controversial. When someone takes it really literally it could be interpreted differently. That is why this question went viral.

發表者: Caesar Aug 25 2015, 02:51

QUOTE (Pearltea @ Aug 25 2015, 10:28 )

QUOTE (Caesar @ Aug 25 2015, 10:16)

I agree - but even on the language's side, it's highly controversial. When someone takes it really literally it could be interpreted differently. That is why this question went viral.

Damn true.

Still a nice question tho ,
in fact I forward'd this to some young kids few months ago,
no wonder most of them hit the bell , but none of them able to present it logically( w/ short n clear answer )

Amazing question that perfectly demonstrated language skill is important even in science subj . ( which I suck

)

發表者: 雞仔嘜 Aug 25 2015, 05:05

May 15, 16, 19
June 17, 18
July 14, 16
August 14, 15, 17

1. a已知月份而說b不知，減去不重覆18,19所在之may,jun
2. b聽a後已知，減去重覆之14餘16jul 15aug 17aug
3. a聽b後再知，即其所知月份只餘一天，即16jul

發表者: Pearltea Aug 25 2015, 13:18

有沒有其他答案或解釋?

發表者: 徐元直 Aug 25 2015, 20:22

QUOTE (Pearltea @ Aug 25 2015, 06:18)

有沒有其他答案或解釋?

嘗試盡量用清晰直觀的語言來解釋。

一開始時已知的，可能的日期：

May 15, 16, 19
June 17, 18
July 14, 16
August 14, 15, 17

1.知道月分的Albert確定僅知道日數的Bernard不可能直接推測出月分，由此可知該月分並不包含只對應該月的日數。May和June均包含只對應該月的日數（18和19），因此可以排除。

~~May~~ ~~15, 16, 19~~
~~June~~ ~~17, 18~~
July 14, 16
August 14, 15, 17

2.知道日數的Bernard聽到第一句話，靠上述推理排除May和June後，馬上能夠確定月分，說明他所知的日數並非剩下月分共有的14日，只能是15、16或17，Bernard由此倒推出是July還是August。

~~May~~ ~~15, 16, 19~~
~~June~~ ~~17, 18~~
July 14, 16
August 14, 15, 17

3.知道月分的Albert聽到上一句話排除14日後，馬上能夠肯定日期，說明他所知月分是只剩唯一可能性的July，而不是還有兩個可能性的August。

~~May~~ ~~15, 16, 19~~
~~June~~ ~~17, 18~~
July 14, 16
August 14, 15, 17

因此生日是July 16th。

發表者: Pearltea Aug 25 2015, 20:54

You guys are correct. The approaches are right.

Here's the alternative solution that readers are arguing over that supports Aug 17:

1. Albert knows that Bernard doesn’t know. (Maybe Cheryl told him as much).
2. Albert deduces Bernard can’t have a unique date such as 18 or 19.
3. Albert, smugly taunts Bernard, announcing Bernard doesn’t know. This is the first statement of the problem.
4. Bernard realises what Albert has realised, which is that Bernard does not have 18 or 19. Now if Albert was holding June he would know the answer, because there is only one remaining date in June, namely June 17. So Bernard deduces it is not June.
5. Bernard announces he knows the answer. This is the second statement of the problem.
6. If Bernard is so confident, he must have a unique date. We know it’s not 18 or 19. What other unique date can it be? There are two 14s, two 15s, two 16s and two 17s - but Bernard has eliminated June 17 - leaving him with August 17 only. That’s how he worked it out.
7. Albert is furious Bernard beat him to the answer. Albert puts himself in Bernard’s shoes, running through the six steps above. Finally Albert reaches the same conclusion we have, Bernard must have 17. Albert announces he knows the answer too.

This is the problem when people take the statements too literally.

However, it is interesting to see how people interpret the cues differently because they were presented in the form of communication instead of listed as known facts. Had I asked my boss (a negotiator) this brain teaser, he would have stopped at "Cheryl gives them a list of 10 possible dates" and said "This woman is obviously playing games. I'm gonna bet my money that her birthday falls on any other date but one of those 10."

發表者: neveryield Aug 29 2015, 04:44

甚麼叫作"直接推測"?

發表者: Pearltea Aug 29 2015, 05:05

QUOTE (neveryield @ Aug 29 2015, 12:44 )

甚麼叫作"直接推測"?

I'm sure he'll respond but it means "to deduce" or "to derive" from the given information...is that what you're looking for?

發表者: 徐元直 Aug 29 2015, 05:26

QUOTE (neveryield @ Aug 28 2015, 21:44 )

甚麼叫作"直接推測"?

參見我樓上的解釋。