The Solutions ~~~~ -littlebird09(小小鸟) @费城华人论坛:费城枫下论坛 The Rolia Forum of Philadelphia

The Solutions ~~~~

littlebird09(小小鸟)

If Sam or Alex had 1 or 10, then they would have solved it straight away. But neither did.

But when Alex discovered that Sam didn't know, he went from not knowing to knowing. So Alex must have had a number where Sam's answer was crucial.

If Alex had 2, then Sam could have 1 or 3 - and the crucial answer "I don't know your number, either" would have ruled out 1, leaving 3 as the other number (Solution: 2 and 3)

Now, if Alex had 3, then he would expect Sam to have either 2 or 4. But if Sam had 2, Sam could have guessed the answer already (because Alex had already said he didn't know, so could not have had 1). When Alex discovers that Sam also doesn't know, he can rule out 2 as the answer. (Solution: 3 and 4).

Exactly the same arguments work at the other end of the range, providing the other two solutions: (Solution: 9 and 8) and (Solution: 8 and 7)

(#7450451@0)
Last Updated: 2012-4-20
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4 solutions -melifeisgoodme(好心情); 2012-4-20 (#7450379@0)

1 candy 4 u :) -littlebird09(小小鸟); 2012-4-20 (#7450395@0)

不是小红旗？ -melifeisgoodme(好心情); 2012-4-20 (#7450446@0)

不喜欢ＣＡＮＤＹ？　～～～ -littlebird09(小小鸟); 2012-4-20 (#7450470@0)

你数学真这么好？ -fly_universe(飞越时空); 2012-4-20 (#7450431@0)

啊，看好题目，凑一下不就好了。。 -melifeisgoodme(好心情); 2012-4-20 (#7450448@0)

哪那么容易。凑了没两回，就已经把自己整迷糊了。 -cute99(behappy); 2012-4-20 (#7450474@0)

给抄下答案撒？！ -cute99(behappy); 2012-4-20 (#7450436@0)

The Solutions ~~~~ -littlebird09(小小鸟); 2012-4-20 {877} (#7450451@0)
If Sam or Alex had 1 or 10, then they would have solved it straight away. But neither did.

But when Alex discovered that Sam didn't know, he went from not knowing to knowing. So Alex must have had a number where Sam's answer was crucial.

If Alex had 2, then Sam could have 1 or 3 - and the crucial answer "I don't know your number, either" would have ruled out 1, leaving 3 as the other number (Solution: 2 and 3)

Now, if Alex had 3, then he would expect Sam to have either 2 or 4. But if Sam had 2, Sam could have guessed the answer already (because Alex had already said he didn't know, so could not have had 1). When Alex discovers that Sam also doesn't know, he can rule out 2 as the answer. (Solution: 3 and 4).

Exactly the same arguments work at the other end of the range, providing the other two solutions: (Solution: 9 and 8) and (Solution: 8 and 7)

how about numbers 5 and 6? -fly_universe(飞越时空); 2012-4-20 (#7450483@0)

那就没有满足这个条件：Alex: Now I know! -melifeisgoodme(好心情); 2012-4-20 (#7450504@0)

Yeah. If Alex has 5, Sam could have 4 and 6, there is no way for Alex to exclude Sam's number from 4 or 6. -littlebird09(小小鸟); 2012-4-20 (#7450515@0)
明白了，看来我语文没你好。。。 -fly_universe(飞越时空); 2012-4-20 (#7450546@0)

我小时候读书读得好。。。 -melifeisgoodme(好心情); 2012-4-20 (#7450563@0)

显摆小时候基础打得好 -fly_universe(飞越时空); 2012-4-20 (#7450572@0)

只限小学。。。 -melifeisgoodme(好心情); 2012-4-20 (#7450579@0)

现在依然显现。。。显摆记性好？ -fly_universe(飞越时空); 2012-4-20 (#7450604@0)

少年天才班的？　：） -littlebird09(小小鸟); 2012-4-20 (#7450586@0)

没去，不让。。。 -melifeisgoodme(好心情); 2012-4-20 (#7450590@0)

谁？　害人呢! -littlebird09(小小鸟); 2012-4-20 (#7450596@0)

幸好没去。。。。 -melifeisgoodme(好心情); 2012-4-20 (#7450599@0)

去了就．．．？　有故事请展开～～～ -littlebird09(小小鸟); 2012-4-20 (#7450621@0)

说明天赋在那。。。 -fly_universe(飞越时空); 2012-4-20 (#7450602@0)

别，我怀疑用脑过度，现在没脑了。。 -melifeisgoodme(好心情); 2012-4-20 (#7450609@0)

现在没脑了，你是说你现在说的是白痴话:-)? -fly_universe(飞越时空); 2012-4-20 (#7450618@0)

有点老年痴呆。。。：） -melifeisgoodme(好心情); 2012-4-20 (#7450622@0)

你是想说我们解答没你好的是连老年痴呆都不如。。。 -fly_universe(飞越时空); 2012-4-20 (#7450646@0)

一般教授都不会做小学生的题目。。。 -melifeisgoodme(好心情); 13:13 (#7450647@0) reply more -melifeisgoodme(好心情); 2012-4-20 (#7450652@0)

too difficult :-( -iou(笨恐龙); 2012-4-20 (#7450381@0)

no worries, I did take a bit time to get it too :-) -littlebird09(小小鸟); 2012-4-20 (#7450414@0)

Alex 2; Sam 3 or Alex 9; sam 8....Am I right? -cute99(behappy); 2012-4-20 (#7450388@0)

smart cute ~~~ hug hug :) -littlebird09(小小鸟); 2012-4-20 (#7450399@0)

我对了啊？！。。。好心情说是4种SOLUTIONS, 我才想出两种，另两种呢？ -cute99(behappy); 2012-4-20 (#7450416@0)

Alex had 3 and Sam 4, Alex 8 and Sam 7 -littlebird09(小小鸟); 2012-4-20 (#7450439@0)

Y -melifeisgoodme(好心情); 2012-4-20 (#7450449@0)
还是没想明白。 -cute99(behappy); 2012-4-20 (#7450453@0)

参见（#7450451@0) -littlebird09(小小鸟); 2012-4-20 (#7450466@0)

+1. I was about to tell this answer. -glow_mm(光彩照人); 2012-4-20 {504} (#7450493@0)
Alex: I don't know your number --> Alex cant be 1 or 10, otherwise it is obviously sam is 2 or 9;

Sam: I don't know your number --> Same cant be 2 or 9: if S is 2, then he shoule know A must be 1 or 3, and from above, A is not 1 so A must be 3; the same when S is 9, A can only be 8 or 10, since S knows A cannot be 10, then A must be 8. In both cases, Sam would have known A's number.

Alex: I now know your number -->Since Sam cannot be 2 or 9, then A must be 3 so S is 4, or A is 8 and S is 7.

right, very good ~! You got 1 candy :-) -littlebird09(小小鸟); 2012-4-20 (#7450519@0)

不会 -vavav(山野兔子); 2012-4-20 (#7450405@0)

笨！ -cute99(behappy); 2012-4-20 (#7450422@0)

hehe~~~ -iou(笨恐龙); 2012-4-20 (#7450454@0)

还笑。。你也一样。呵呵 -vavav(山野兔子); 2012-4-20 (#7450475@0)

hehe... -cute99(behappy); 2012-4-20 (#7450481@0)

呵呵～～～ -littlebird09(小小鸟); 2012-4-20 (#7450455@0)
me, either. -healthy321(领导说:做人要低调.); 2012-4-20 (#7450877@0)

小学没毕业的掩面逃走。 -snow_bird(sunshine); 2012-4-20 (#7450513@0)

hahaha~~~~ don't run away, try harder :) -littlebird09(小小鸟); 2012-4-20 (#7450517@0)

嘿嘿, 主要是看你已经公布答案了, 我就不用动脑子了 :-)... -snow_bird(sunshine); 2012-4-20 (#7450561@0)

lazy girl ~~ not your style though :) -littlebird09(小小鸟); 2012-4-20 (#7450580@0)

大学毕业不会做的飘过。 -princemeetsprincess(西门小鸟); 2012-4-20 (#7450537@0)

飘哪儿去?　注意安全哦　：）～～～ -littlebird09(小小鸟); 2012-4-20 (#7450584@0)

Alex9 & Sam 8, or Alex 2 Sam 3 -appleclassical(hallelujah); 2012-4-20 (#7450562@0)

Yeah, you got 2 answers, there are 2 more solutions :) -littlebird09(小小鸟); 2012-4-20 (#7450578@0)

晕菜...比那啥还费脑子...:) -jesse_dd(紫飞鱼); 2012-4-20 (#7450581@0)

哈哈,　不容易啊，　把小鱼都绕晕了　～～～ -littlebird09(小小鸟); 2012-4-20 (#7450594@0)

她是高手。。。 -melifeisgoodme(好心情); 2012-4-20 (#7450598@0)

I know, very smart girl :) -littlebird09(小小鸟); 2012-4-20 (#7450612@0)

Alex: 2, Sam:3; or Alex:9,Sam:8 ~~ -sr-71(Black); 2012-4-20 (#7450597@0)

Yeah, you got 2 answers, there are 2 more solutions :) -littlebird09(小小鸟); -melifeisgoodme(好心情); 2012-4-20 (#7450611@0)

haha, 留你的　～～～ -littlebird09(小小鸟); 2012-4-20 (#7450614@0)
Alex: 2, Sam:3; or Alex:9,Sam:8; or Alex3 Sam2, or Alex8 Sam 9 ~ ~ -sr-71(Black); 2012-4-20 (#7450619@0)

NO, NO, NO...... Try harder :) -littlebird09(小小鸟); 2012-4-20 (#7450645@0)

答错扣分。。。 -melifeisgoodme(好心情); 2012-4-20 (#7450654@0)

你当老师学生就可怜罗～～～～～ -littlebird09(小小鸟); 2012-4-20 (#7450680@0)

Alex: 2, Sam:3; or Alex:9,Sam:8; or Alex3 Sam4, or Alex8 Sam 7 ~ ~ 回答完毕，累死我了 -sr-71(Black); 2012-4-20 (#7450671@0)

辛苦了，　给你两棵ＣＡＮＤＹ，再加一面小红旗　：） -littlebird09(小小鸟); 2012-4-20 (#7450673@0)

不公平。。。好心情第一个交卷 100分才得一个candy. 我50分什么也没得。 -cute99(behappy); 2012-4-20 (#7450681@0)

见色忘义。。 -melifeisgoodme(好心情); 2012-4-20 (#7450684@0)

哼, 挑拨离间 ~!!!! -littlebird09(小小鸟); 2012-4-20 (#7450695@0)

ＨＵＧ　不算？他们都没有的!~~~~ -littlebird09(小小鸟); 2012-4-20 (#7450688@0)

hug 当然算。。。好心情也得hug了吗？ -cute99(behappy); 2012-4-20 (#7450707@0)

不可能 ! 只有你有, 高兴点没? ~~~ :-) -littlebird09(小小鸟); 2012-4-20 (#7450721@0)

高兴，高兴。。。。要不你也鼓励一下心情哥？！ -cute99(behappy); 2012-4-20 (#7450737@0)

我怕嫂子不高兴 ~~~~~ 哈哈哈~~~ -littlebird09(小小鸟); 2012-4-20 (#7450745@0)

是哦。 -cute99(behappy); 2012-4-20 (#7450771@0)
经申请，嫂子说，没事，注意安全就好。。 -melifeisgoodme(好心情); 2012-4-20 (#7450785@0)

准备好了? -littlebird09(小小鸟); 2012-4-20 (#7450793@0)

压力很大。。。 -melifeisgoodme(好心情); 2012-4-20 (#7450860@0)

那就算了～～～　对了,　小香找你补习～～～　找个数学最好的给我洗洗脑就行了～～～ :D -yoyo23(纯水有香); 13:42 (#7450850@0) reply more -littlebird09(小小鸟); 2012-4-20 (#7450878@0)

我这两块糖都给你，我自己只留一面小红旗 ~ ~ -sr-71(Black); 2012-4-20 (#7450696@0)

好。。。。下回得好处不要独吞哈。 -cute99(behappy); 2012-4-20 (#7450730@0)

哪会独吞啊，我都给你留着呢 ~ ~ -sr-71(Black); 2012-4-20 (#7450741@0)

不要啊，压力很大。。。一会让啊香知道了，你没法交代。 -cute99(behappy); 2012-4-20 (#7450760@0)

没事，姐姐尽管拿着。这小抠儿一般不让东西给人的，好容易让了一次，你可千万别再给他机会反悔啊～～～:D -yoyo23(纯水有香); 2012-4-20 (#7450859@0)

小抠儿?哈哈 -melifeisgoodme(好心情); 2012-4-20 (#7450863@0)

Good job! 。。。。 -cute99(behappy); 2012-4-20 {25} (#7450623@0)
50分。 Better than 兔子。

哈哈,　可怜的兔子～～～ -littlebird09(小小鸟); 2012-4-20 (#7450630@0)

哈。。。没关系，咱物理好 -vavav(山野兔子); 2012-4-20 (#7450649@0)

好好好!　以后有物理题问你　～～～　：） -littlebird09(小小鸟); 2012-4-20 (#7450686@0)

在打开你这个贴之前，我做了个聪明的决定。先吃饭～～～免得撞墙撞晕了把饭浪费了～～～现在我要去撞墙了 -yoyo23(纯水有香); 2012-4-20 (#7450740@0)

亲爱的,　别担心, 给你个CANDY　压压惊先　～～～ -littlebird09(小小鸟); 2012-4-20 (#7450792@0)

有糖吃，那就不撞墙了。一会儿找个数学最好的给我洗洗脑就行了～～～ :D -yoyo23(纯水有香); 2012-4-20 (#7450850@0)

我帮你找好心情　～～～ -littlebird09(小小鸟); 2012-4-20 (#7450871@0)

haha -healthy321(领导说:做人要低调.); 2012-4-20 (#7450896@0)

笑了？没给钱就笑了？ ~~~~~~ -yoyo23(纯水有香); 2012-4-20 (#7451049@0)

我看了大家的回帖，决定不看了 -qiluoxiang(绮罗香); 2012-4-20 (#7451028@0)

呵呵，你可别跟我比，我是数学白痴来着～～～ -yoyo23(纯水有香); 2012-4-20 (#7451051@0)

@Philadelphia

The Solutions ~~~~

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