An usual day at unusual school (answers)
I was captivated at the website which Yi Chen linked us to, @ http://www.c3.lanl.gov/mega-math/workbk/logic/loplay.htmlso..... i decided to do an analysis on who actually is a brave and who actually is a bright. this analysis would not have been complete with the great help of Yi chen (who actually solved the ones which i do not know. he also actually solved the puzzle in the end). so thanks alot to Yi chen. anyone who is interested, go to the link and read the play. its real interesting and will bring sense to whatever im abt to say."
And here's the real story: now we see from scene 3 that Mr. Bumbleton is actually a brave, by stating that "you have not yet decided which one you will be" when obviously he actually did. so...back to scene 1, we realise that Ms. smart is a bright, since mr. bumbleton, the liar, stated that she lied.
Now we figured out the basics, lets move on to analysing the charaters in scene 2. Ms. Boss is obviously a Brave.
now we move on from desk to desk.
jan and mikes are brights. you can see as if jan was a brave, her sentence would have translated: "Brights would always say that they r braves", which make no sense at all. mike just sorts of repeats what jan says, so he is actually a bright too.
Pat and Denise can be bright and braves. There's actually no way we can say which is which. The key point is that they two cannot be the same. Since Pat said that Denise is a Brave, and if Pat is a bright, Denise would be a brave and if Pat is a brave, he will accuse Denise to be a brave while she is not. In any case they must be of different kinds and hence this pair will not affect the final count there's no need to find out which is which.
John and Emily. this one is quite easy. assume that john is a bright. what he said would be perfectly true. but is he was a brave, and emily can be anything else (bright or brave), the whole thing would not make sense.
Billy must be a bright here. if billy was a brave, then there would 2 braves or no braves at all, since he lied that "Exactly one of us is a Brave". but if there are no braves at all, billy himself is a brave. if there are 2 braves all together, susan wouldnt be saying that billy is a brave, cause then she would be telling the truth. so the only explanation is that billy is a bright. susan is lying about billy is being a brave, so she is a brave.
Pete and Sandra gave very little information, but i managed to guess it in the end. You see, that pete is a brave because he said "OK, OK, then, we're both Braves. Now leave us alone! ". if he was a bright, he would have told the truth, that he is a bright. so this shows that he is a brave. But if they are both braves, pete would be telling the truth. So now the only logical explanation left is that pete lied about both of them being braves, which leaves Sandra a bright.
Alice might be a brave or a bright, but Dan must be a bright. If Alice is a bright, then her first sentence would be true, which makes Dan a bright as well. If she is a brave, it means that they are of different types and since she is the brave, Dan will still be a bright. There's no way that we can knoe if Alice is bright or brave though.
Mark and Pam can be anything. Since they both claim to be brights. A bright would claim to be a bright as it is the truth. A brave would also claim to be a bright since braves always lies.
Tonny is a bright, while Becky is a brave. If Tonny was a brave, the fact would be that both of them are braves, because he lied about Becky being the only brave. But if both are braves, then Susan will not say that Tonny is a brave bacause by saying so, she would be telling the truth. So, the couclusion is that Tonny was telling the truth, and Becky is a brave.
Tom and Connie is pretty interesting. the first 4 questions dont tell much, as both braves and brights would have had the same answer. but from the last question, is somebody lying, we can see that tom is inconsistent with his answers. since braves lie to everything, and we assume that tom was a brave, tom would have lied that his partner is a brave in the 3rd question. and at the 4th question, there IS somebody lying (that is tom himself), so he has to lie that no one was lying, thus the contradiction in tom's answers. connie is a bright as her answers dont contradict and makes sense with all the things tom said(or lied about).
That's the character evaluation of the whole story. Here's the list:
Ms Smart: bright
Bumbleton: brave
Ms Boss: brave
Jan: bright
Mike: brave
Pat: bright
Denise: brave
John: bright
Emily: brave
Billy: bright
Susan: brave
Sandra: bright
Pete: brave
Alice: bright/brave
Dan: bright
Mark: bright/brave
Pam: bright/brave
Tony: bright
Becky: brave
Tom: brave
Connie: bright
Total number of people (excluding Terry): 21
There are three possible cases (excluding Alice) :
9 brights and 11 braves
10 brights and 10 braves
11 brights and 9 braves
At the end of the story, Terry said that there are 11 brights and 10 braves. I will now conclude it case by case.
Case one: no matter if Alice is a bright of brave, 9 brights and 11 braves cant become 11 brights and 10 braves. Terry got the answer wrong, and become a brave.
Case two: Alice is a bright, making 10 brights and 10 braves to be 11 brights and 10 braves. Terry got the answer correct, and he become a bright.
Case three: Alice is a brave, making 11 brights and 9 braves to be 11 brights and 10 braves. Terry got the answer correct, and he become a bright.
To make the whole puzzle seem reasonable and let me and Wang Cong have a sense of accomplishment, we say that Terry is a bright. Yeah that's it, we solved it.
The End
the genii (english spelling of geniuses[ok that was to show of]) who actually solved the puzzle: Lin Yi Chen ,Yu Wang Cong
posted by 望聪 @ 8:13:00 PM
1 Comments:
Actually you CAN figure out Mark/Pam - because of the wording. Mark and Pam have to be brights, because a brave IS the type who would claim to be a bright, so if they raised their hands, they would be telling the truth; therefore, they are brights. It's all in the word "claim"
Post a Comment
Subscribe to Post Comments [Atom]
<< Home