MacRumors Forums Can anyone get this tricky math problem?

Feb 9, 2008, 12:45 AM   #26
CalBoy
macrumors 601

Join Date: May 2007
Quote:
 Originally Posted by Doctor Q A bookshelf has three encyclopedia volumes: A-I, J-R, and S-Z. They are in the usual order, left to right on the shelf. The covers are 1/16" thick. Each book has pages numbered 1 to 1000. Each sheet of paper is 1/250 of an inch thick. If a bookworm chews its way from page 1 of the A-I volume through page 1000 of the S-Z volume, how far did it travel? (You may decide whether or not the bookworm ate the starting page and the ending page; use whichever assumption makes your computation easier.)
Quote:
 Originally Posted by swiftaw 6.25 inches
I got this as well, but something about this whole thing makes me think that Doctor Q is going to do something clever and show us how wrong we are.
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Feb 9, 2008, 06:53 AM   #27
creator2456
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Join Date: Jul 2007
Location: Chicago
Quote:
 Originally Posted by swiftaw 6.25 inches
((500pages x 3books) x .004") + (4covers x .0625") = 6.25"

(7girls x 2legs) + (7girls x 7backpacks x 7big cats x 4legs) + (7girls x 7backpacks x 7big cats x 7small cats x 4legs) = 10990legs
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Last edited by creator2456; Feb 9, 2008 at 07:01 AM. Reason: added legs problem
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Feb 9, 2008, 07:53 AM   #28
Zwhaler
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Join Date: Jun 2006
Quote:
 Originally Posted by dobbin I don't see why this is at all hard. It seems very simple to me. 7 girls --> 14 legs 7x7 = 49 backpacks 49x7 = 343 big cats --> 1372 legs 343x7 = 2401 little cats --> 9604 legs 14+1372+9604 = 10990 legs in total
I did the exact same thing. Got it on my first try Im cool
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 Feb 9, 2008, 08:07 AM #29 yippy macrumors 68020     Join Date: Mar 2004 Location: Chicago, IL Doh!, you guys are right, you only need 500 pieces of paper to get 1000 pages. In that case the answer is 6.25" 0
 Feb 9, 2008, 11:54 AM #30 SilentPanda Moderator emeritus     Join Date: Oct 2002 Location: The Bamboo Forest There could be 501 pages per book if, after opening the cover you see that the first page facing you is blank, flipping that you see pages 1 and 2, then 3 and 4, until you get to the end which has 999 and 1000. Flipping 1000 would leave a blank side of the page. Which would be 501 pages per book. They might do that in order to not have the ink rub off from page 1 or 1000 onto the harder outside of the book. Poor little inch worm would have to inch 3/250ths further! __________________ My 24 hour web cam! ʕノ•ᴥ•ʔノ ︵ ┻━┻ And remember. 0
 Feb 9, 2008, 12:52 PM #31 jsw Moderator emeritus     Join Date: Mar 2004 Location: Andover, MA Explanation (highlight to see): The books (square brackets indicate covers): [A-I][J-R][S-Z]The amount chewed through: ][J-R][Why? Because the first page of A-I is to the right on the shelf, and the last page of S-Z is to the left. So four covers plus, as has adequately been explained, 500 pages. 4x(1/16) + 500x(1/250) = 4/16 + 500/250 = 1/4 + 2 = 2.25". As per Nermal. I just felt it was time to explain. __________________ You'll be the one moaning for me to give you some. - THC(taken out of context) Last edited by jsw; Feb 9, 2008 at 02:39 PM. Reason: No ruining of the fun.... 0
 Feb 9, 2008, 01:54 PM #32 Nermal Moderator     Join Date: Dec 2002 Location: Whakatane, New Zealand I was kind of hoping Q would come along and say "Nermal's right, now figure out why" but you had to go and ruin that, didn't you? 0
Feb 9, 2008, 02:27 PM   #33
CalBoy
macrumors 601

Join Date: May 2007
Quote:
 Originally Posted by jsw As per Nermal. I just felt it was time to explain.
I knew I wasn't right for some reason.

Quote:
 Originally Posted by CalBoy I got this as well, but something about this whole thing makes me think that Doctor Q is going to do something clever and show us how wrong we are.
You ruined the prophecy jsw! Only Doctor Q was to show us the way!
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 Feb 9, 2008, 02:36 PM #34 skyrider007 macrumors 65816     Join Date: Aug 2007 Location: Bangkok this is fun! __________________ 15.4" MacBook Pro 2.0GHz i7 iPad 3G iPod Touch 16GB (2G) BlackBerry Bold 9780 (white) 0
Feb 9, 2008, 02:39 PM   #35
aquajet
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Join Date: Feb 2005
Location: VA
Quote:
 Originally Posted by jsw Why? Because the first page of A-I is to the right on the shelf, and the last page of S-Z is to the left.
To be fair, Dr. Q said the volumes were "in the usual order, left to right". He didn't say anything about whether or not any of the volumes were shelved upside down.
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Feb 9, 2008, 02:40 PM   #36
jsw
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Join Date: Mar 2004
Location: Andover, MA
Quote:
 Originally Posted by Nermal I was kind of hoping Q would come along and say "Nermal's right, now figure out why" but you had to go and ruin that, didn't you?
Fine, fine, I white-texted it.

I just wanted your brilliance to be proven correct.
Quote:
 Originally Posted by CalBoy You ruined the prophecy jsw! Only Doctor Q was to show us the way!
You assume we're different people, now, don't you?
Quote:
 Originally Posted by aquajet To be fair, Dr. Q said the volumes were "in the usual order, left to right". He didn't say anything about whether or not any of the volumes were shelved upside down.
You make a good point - they might also have been laid flat, in which case we'd need the width and/or height of the paper as well as information about the binding, which wasn't provided.
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 Feb 9, 2008, 03:01 PM #37 Doctor Q Administrator     Join Date: Sep 2002 Location: Los Angeles blood donor center I was waiting for someone to post the correct answer AND an explanation. Nermal was first with the answer, jsw with the explanation. The cute friendly bookworm says thanks for the snack. __________________ I support the MacRumors Blood Drive! 0
 Feb 9, 2008, 03:37 PM #38 fridgeymonster3 macrumors 6502   Join Date: Jan 2008 I got the answer on my first try. It was pretty easy; however, I don't think we should be bragging it was easy since it is for 5th graders. I mean, come on, post something challenging! __________________ "Even in my sleep-deprived state, I've managed to pull off another one of my classic pranks. BAZINGA!" 0
Feb 9, 2008, 03:41 PM   #39
CalBoy
macrumors 601

Join Date: May 2007
Quote:
 Originally Posted by fridgeymonster3 I mean, come on, post something challenging!

There are 3 doors. Behind 1 door lies immense wealth and riches. Behind the other two lie certain death.

A guard asks you to choose a door and you pick #2. The guard then reveals to you what's behind Door #1 and you see that behind it was one of two chances of certain death.

The guard now asks you if you would like to change your selection from Door #2 to Door #3.

Mathematically is there a probability increase that benefits you if you change doors?

BTW, I don't know the answer to this, but I've seen it thrown around a few times
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Feb 9, 2008, 03:41 PM   #40
jsw
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Join Date: Mar 2004
Location: Andover, MA
Quote:
 Originally Posted by fridgeymonster3 I got the answer on my first try. It was pretty easy; however, I don't think we should be bragging it was easy since it is for 5th graders. I mean, come on, post something challenging!
Pick any of these and report back with the answer!
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Feb 9, 2008, 03:45 PM   #41
WildCowboy

Join Date: Jan 2005
Quote:
 Originally Posted by CalBoy Mathematically is there a probability increase that benefits you if you change doors?
Yes, very much so.
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Feb 9, 2008, 03:46 PM   #42
CalBoy
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Join Date: May 2007
Quote:
 Originally Posted by WildCowboy Yes, very much so.
Darn it! You weren't supposed to say anything!
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Feb 9, 2008, 03:47 PM   #43
jsw
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Join Date: Mar 2004
Location: Andover, MA
Quote:
 Originally Posted by CalBoy Mathematically is there a probability increase that benefits you if you change doors?
Yes!

Edit: damn it! Darned kids forcing me to make them fruit smoothies and slowing down my response time. Grrr. In a few months, though, I shall prevail!
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Feb 9, 2008, 03:48 PM   #44
WildCowboy

Join Date: Jan 2005
Quote:
 Originally Posted by jsw Yes!
Stop copying off of my paper!
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 Feb 9, 2008, 03:52 PM #45 Doctor Q Administrator     Join Date: Sep 2002 Location: Los Angeles blood donor center Can you prove which is larger, e^pi or pi^e, using properties of those numbers rather than simply computing the exponentials? It's a real question, not a trick. I had this problem on a test. If only I could remember the answer! __________________ I support the MacRumors Blood Drive! 0
Feb 9, 2008, 03:52 PM   #46
kosmo
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Join Date: Apr 2002
Location: Atlanta
Quote:
 Originally Posted by CalBoy Ok, since you asked. There are 3 doors. Behind 1 door lies immense wealth and riches. Behind the other two lie certain death. A guard asks you to choose a door and you pick #2. The guard then reveals to you what's behind Door #1 and you see that behind it was one of two chances of certain death. The guard now asks you if you would like to change your selection from Door #2 to Door #3. Mathematically is there a probability increase that benefits you if you change doors? BTW, I don't know the answer to this, but I've seen it thrown around a few times
Yes, your odds are increased by changing doors as "odd" as that seems. The first time you select a door you have a 1/3 chance of picking the right door and a 2/3 chance of picking the wrong door. After a wrong door has been revealed to you, the door you picked still has a 1/3 chance of being right however the other door now has a 2/3 chance of being right. Change doors!
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Feb 9, 2008, 03:57 PM   #47
fridgeymonster3
macrumors 6502

Join Date: Jan 2008
Monty Hall problem...real creative . Now if one of us explained that in a simple format without links to wikipedia (or borrowing any of their descriptions/examples) that would be much more impressive. My father taught statistics & probability at a graduate school and explained it in very simple terms before wikipedia existed which made it easy (not that me the psychology major, law school student could understand ).

Quote:
 Originally Posted by jsw Pick any of these and report back with the answer!
sure i'll solve those and get back to you.....in say, when some else figures them out, I pounce on their answers, and post them here first
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Last edited by WildCowboy; Feb 9, 2008 at 03:59 PM. Reason: post merge
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Feb 9, 2008, 04:01 PM   #48
WildCowboy

Join Date: Jan 2005
Quote:
 Originally Posted by fridgeymonster3 Now if one of us explained that in a simple format without links to wikipedia (or borrowing any of their descriptions/examples) that would be much more impressive.
What, you're looking for real effort out of us?!

Why reinvent the wheel when Wikipedia already has a good, thorough explanation?
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 Feb 9, 2008, 04:07 PM #49 EricNau Demi-God (Moderator emeritus)     Join Date: Apr 2005 Location: San Francisco, CA I love this one: Give the next two numbers in this sequence: 9, 10, 11, 12, 13, 14, 21, ... 0
Feb 9, 2008, 04:08 PM   #50
jsw
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Join Date: Mar 2004
Location: Andover, MA
Quote:
 Originally Posted by Doctor Q Can you prove which is larger, epi or pie?
This is quite easy to do visually with no math.

Epi:

Pie:

I think the visual cues allow it to be easily shown that the Epi is much smaller than a typical pie.
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