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« Photoblogging the Wash State Election Protest | Main | "My name's Rather. I'm a dick." »
January 12, 2005

Another Math Puzzler

What is this? The Corner? (I wish.)

Okay, since that last puzzle got so many responses, let me offer another one.

I will caveat this first: This one is pretty easy. The real math-heads here are going to laugh at this one. This is really a middle-school sort of problem... but then, a lot of you have probably forgotten all math past middle-school.

And it bothered me a lot when I heard it as a kid. So here we go:

Three men walk into a hotel. They ask how much it will be to share a room. They're told it's thirty dollars. (Umm... it's a crap hotel. In Honduras. Okay?)

So each man ponies up ten dollars to the concierge and then goes up to the room.

After taking the money, the concierge realizes that he's over-charged the men-- it's the weekend, and the rate for a single room should be twenty five dollars. So he summons the bellboy, gives him five singles, and tells him to deliver the men their refund.

Well, as the bellboy's going up the stairs, he realizes that five dollars is going to be hard to divide between three people. So he decides he'll just tell the men the actual rate was $27, give the men each a single dollar back, and pocket $2 as his reward for helping the men avoid a lot of squabbling over who's going to get shorted on the refund.

And that's what he does.

Now, each man paid nine dollars for the room. Three times nine is twenty seven, and there's two more dollars in the bellboy's pocket.

27 plus two more in the bellboy's pocket equals twenty-nine dollars total. But they paid $30 originally. Where did the dollar go?

Hint: Actually, I guess this isn't so much a math problem as flim-flam problem.

A Non-Math Puzzle: In your basement you have a light. There are three light-switches on your first floor, one of which turns on that light, but you don't know which. (The other two are dead switches which no longer operate anything in the house.)

You cannot see the light from the first floor of your house.

How can you tell which switch controls the light by making only a single trip down to the basement to check the light?


posted by Ace at 12:22 AM
Comments



The question that's on my mind is why are three grown men staying in a single room in Honduras? Did Andrew Sullivan have something to do with this?

Posted by: PlacidPundit on January 12, 2005 12:49 AM

We start with each man having donated $10. $10+$10+$10=$30. The proprietor now has $30 in his register.

He now gives the bellboy $5. There's now $25 in the proprietor's register, and $5 in the bellboy's pocket. So we start with the $25 sitting in the register.

Now, using the $25 as our starting point, the bellhop has the $5 in his pocket, which added up equal $30. We've simply divided the total in two distinct places.

Now, the bellhop gives $1 to patron A (that makes $4 in the bellhop's pocket, $25 in the register and $1 in A's pocket).

The bellhop gives another $1 bill to patron B. We still have $30, but now dispersed in 4 places (one in A's pocket, one in B's pocket, 3 in the bellhop's pocket and $25 still sitting in the register).

Now the bellhop completes his endgame, by delivering up $1 for patron C.

Now we have $30 in 5 separte places:

$25 in the register;
$2 in the bellhop's pocket;
$1 in A's pocket;
$1 in B's pocket; and,
$1 in C's pocket.

We still have $30.

Now A, B and C have enough money among them to last about 10 minutes at a tity bar.

No mystery, just a slight-of-hand logic problem.

Bravo for bringing this one back to life. I forgot all about it.

That's just the way it fucking is.

Posted by: KCTrio on January 12, 2005 12:50 AM

They bought pancakes.

Brown ones.

See, the golden ones were a dollar extra, so they went for the special.

Posted by: Dogstar on January 12, 2005 12:50 AM

the three men have already paid 25. the bellboy gives each man 3 bucks. then he pockets 2 for himself. 25+3+2=30

Posted by: amish on January 12, 2005 12:50 AM

The original $30 no longer has anything to do with it.

The three roommates are out $27, the hotelier has $25, and the bellboy's got $2.

Posted by: Patton on January 12, 2005 12:51 AM

WIth $25 in the register, each man has paid his share of $8.33. They each get back a dollar... leaving the total money accounted for at $9.33 a piece. That leaves $.66 per man, or $2, which is in the bell boy's pocket.

Posted by: Dave on January 12, 2005 12:54 AM

Amish:

I like your simplicity of explanation. It's got substance. It's got character.

You're ability to employ concise English has got me crazier than a shithouse rat.

Do you want me to bring Vinny Falcone down here and get your shit together? Well, do you?

Dispense with the concise verbage, and let your prose soar, or rather grow like a fungus, or there'll be hell to pay.

Posted by: KCTrio on January 12, 2005 12:55 AM

would it be cheating to feel of the light bulbs? cause if you can,you could probably turn a couple of them on one at a time and then go check out how warm they are... ya got me im stumped

Posted by: amish on January 12, 2005 01:01 AM

Turn on switches 1 and 2. After a few minutes, turn off switch 2.

Go down to the basement. If the light is on, it's switch 1. If the light is off, but warm, it's switch 2. If the light is off and cold, it's switch 3. Careful not to hit your head or trip over that box.

Posted by: Dead Parrot James on January 12, 2005 01:02 AM

Well... yes...

But what is wrong with the math *I* offered?

Posted by: ace on January 12, 2005 01:02 AM

dead parrot James,

Correct.

Amish,

Correct too, but a lot of "loose shit" in the presentation of your solution.

Posted by: ace on January 12, 2005 01:07 AM

Ace:

There's nothing wrong with the math you offered, it's just irrelevant to solving the problem. There's no mulitplication involved in this exercise. It's all addition and logic. The fact that 9X3=27 has no relevance to solving this problem.

Amish: Why are you stumped when you solved the problem? Dead Parrot just flushed out your solution.

Do you see what I mean about crafing more verbose posts? Do it, or I'll ream your fucking ass like a fucking hammer.

Posted by: on January 12, 2005 01:08 AM

What row of numbers comes next?

1
11
21
1211
111221
312211
13112221

Posted by: amish on January 12, 2005 01:09 AM

Yes, my math is irrelevant and deceptive. That's the flim-flam part.

Here's the deception:

It is actually correct to say three times nine is 27. That is, of course, what they paid. But their actual discount was only three dollars, not the two dollars stolen from them and in the bellboy's pocket.

So the correct way to say it is three times nine is twenty seven, plus the three dollars they got back, equalling thirty dollars, the original price.

"Three times nine is twenty seven plus the two in the bellboy's pocket" adds the wrong and irrelevant term, 2, to the sum.

Posted by: ace on January 12, 2005 01:12 AM

Or, the way to say it with the "2" figure is to say:

"Three times nine is twenty seven, MINUS the two dollars stolen from them, which equals the TWENTY FIVE dollars they're supposed to be paying."

The trick comes from mixing up the two different ways of getting at a right answer-- subtracting 2 to get down to 25, or adding three to get up to 30.

Posted by: ace on January 12, 2005 01:16 AM

Ace:

You are the only important person on that screen. And your explaination is the only one that is lucid, with integrity. Mine was completely fucked up.

I as a member of the posting community am only important in the totality.

I'm shrugging my shoulders as i write this.

I guess I fucked up.

Posted by: on January 12, 2005 01:17 AM

The trouble was you gave me "ideas."

Well, I didn't ask for ideas, I want to know what went fuckin' wrong and how to fix it.

Posted by: ace on January 12, 2005 01:18 AM

Whoever whips out the first Paul Anka quote in the Monty Hall debate is the person I will go to the grave believing.

"You have a 2/3 chance of winning by switching. That's just the fucking way it is."

Posted by: chris on January 12, 2005 01:26 AM
1 11 21 1211 111221 312211 13112221
OOH! Patterns. That one's easy though, just keep summing and flipping.

I'll go find you guys a good spatial/pattern recognition quiz...

Posted by: fat kid on January 12, 2005 01:27 AM

Forgot to mention and adding.

Posted by: fat kid on January 12, 2005 01:27 AM

I got a 96% on this test drunk and ornery.

Check it out.

This is one of those things I blogged about a while ago

Posted by: fat kid on January 12, 2005 01:30 AM

fatkid-summing and flipping?

heres an easy one:


"This is an unusual paragraph. I'm curious how quickly you can find out what is so unusual about it? It looks so plain you would think nothing was wrong with it! In fact, nothing is wrong with it! It is unusual though. Study it, and think about it, but you still may not find anything odd. But if you work at it a bit, you might find out! Try to do so without any coaching! "


Posted by: amish on January 12, 2005 01:35 AM

Good one, but a very well-known chestnut.

In blah-blah school I had to attend a diversity sensitivity thing (no, it wasn't just me, it was everyone on my journal), and they gave me this puzzle.

It was just a paragraph. And you had to count the number of "e's" in it.

No trick.

But the thing is, EVERYONE GOT DIFFERENT ANSWERS. And I was sure I was right, but everyone else found more e's than I did; I double checked and got the same count.

But people had ten more e's than me.

And it turned out they were more right than me-- there were even more than they thought.

What that had to do with diversity is a little tenuous. Still-- kinda freaked me out. You'd think I could count the number of "e's" in one medium-length paragraph.

Posted by: ace on January 12, 2005 01:40 AM

"Whoever whips out the first Paul Anka quote in the Monty Hall debate is the person I will go to the grave believing."

Do you get full value on Door Number 3? Well I want full value on Door Number 1.

Posted by: ace on January 12, 2005 01:51 AM

PAUL ANKA: Alright, you want Door A, Door B, or Door C?
TIMID PAUL ANKA: Hey, let's go! Don't make a maniac out of me!
CONTESTANT: OK, I’ll take Door A.
PAUL ANKA: OK, let's look behind Door B. (Door B is opened, revealing a donkey) A donkey? There's some loose shit going on around here. So, contestant--do you want your door?
CONTESTANT: I guess I’ll switch.
PAUL ANKA: Switch? What was wrong with Door A?
CONTESTANT: Well I just thought--
PAUL ANKA: You thought, you thought, you thought eight things tonight!

Posted by: on January 12, 2005 02:30 AM

The Paul Anka problem:

PAUL ANKA: Alright, you want Door A, Door B, or Door C?
TIMID PAUL ANKA: Hey, let's go! Don't make a maniac out of me!
CONTESTANT: OK, I’ll take Door A.
PAUL ANKA: OK, let's look behind Door B. (Door B is opened, revealing a donkey) A donkey? There's some loose shit going on around here. So, contestant--do you want your door?
CONTESTANT: I guess I’ll switch.
PAUL ANKA: Switch? What was wrong with Door A?
CONTESTANT: Well I just thought--
PAUL ANKA: You thought, you thought, you thought eight things tonight!

Posted by: chris on January 12, 2005 02:31 AM

Uh, I don't know what happened there, but I didn't just steal some anonymous person's material. Loose shit.

Posted by: chris on January 12, 2005 02:32 AM

Uhhhh... Ace, there are no "e's" in that paragraph. That's the unusual part. "E" is the most common letter used in the English language, so for it not to be used in a fairly lenghty paragraph is uncommon.

Posted by: magnetism87 on January 12, 2005 02:44 AM

magnet:

I know. Sorta why I said "EEEEasy."

The thing about counting the number of "e's" wasn't directly related to that. It just reminded me of that exercise.

Posted by: ace on January 12, 2005 02:49 AM

And the next number in the sequence is 1113213211
Each of the numbers in the sequence describes the previous in order. So:
1=one 1 (11)
11= Two 1's (21)
21= One 2, one 1 (1211)
1211= one 1, one 2, two 1's (111221)
etc.


Here is another brain teaser:

Given the obvious: 1/2 = 1/2, and that 3 > 2
(i.e., 3 is greater than 2). So:
1/2 = 1/2
therefore: log(1/2) = log(1/2)
therefore: 3log(1/2) > 2log(1/2)
therefore: log(1/2)^3 > log(1/2)^2
therefore: log(1/8) > log(1/4)
therefore: 1/8 > 1/4
therefore: 1 > 2


Where is the fallacy?


Posted by: magnetism87 on January 12, 2005 02:53 AM

It's my favorite phallacy, the same one that convinced my girlfriend that a 3" log > 7" log.

Posted by: sulla on January 12, 2005 03:49 AM

Damn, this is turning into The Corner. Next thing you know, my couch will be telling me to post comments about Animal House, the Simpsons, or episodes of the original Star Trek series.

(And if ace--posting math problems--is the Derb around here, who's the KJL who cracks the whip and runs the show?)

Posted by: Sean M. on January 12, 2005 04:04 AM

http://www.amazon.com/exec/obidos/ASIN/0385495382/qid=1105521224/sr=2-1/ref=pd_ka_b_2_1/002-9652950-5832025

Posted by: jer on January 12, 2005 04:13 AM

Slice the basement bulb off with a fucking hammer. Duct tape a bomb to the dangling wires. Now go upstairs and try the switches one at a time. When you hear a loud noise, that was the right switch.

Posted by: Kingslasher on January 12, 2005 06:36 AM

Send Joe to the basement checking the fucking light switches so he can get back and report to Mr. Anka, the only important person in that word problem.

You thought you had the answer? You thought, you thought, you thought eight things tonight. But you were only supposed to think one thing. Do I have to get Vinny Falcone out front to ride your asses?

Now does Mr. Anka get his answer or are you going to make a fucking maniac out of him?

Where's Joe?

Posted by: Jimmie on January 12, 2005 08:33 AM

Hmm, your Geek Title Holder has a math puzzle that takes about 2 pages worth of answer. Years ago my husband called me from work with it -- someone's girlfriend got it from her math teacher -- and no one in his office could figure out the answer. It took me one hour to come up with the solution (GEEK). Anybody want a little pain?

Later,
bbeck

Posted by: bbeck on January 12, 2005 09:24 AM

Boy was I off on the wrong track with that light switch problem. I figured you get you a Abu Ghraib prisoner and wire his two fingers into the outside switches and shove a copy of the Gonzales/Bybee memo up under his nutsack and start hitting the switches or something.

We had a similar problem with the pool lighting, but the landscapers fixed it using one of their many children and a bucket of water. Funniest goddamn thing...

Posted by: spongeworthy on January 12, 2005 09:36 AM

this one is loads of fun, math is great:

Find the global minimum to ten decimal places:

f(x,y) = esin(50x) + sin[60ey] + sin[70sin(x)] + sin[sin(80y)] - sin{10(x + y)] + 1/4(x2 + y2)

Posted by: johnnyH on January 12, 2005 10:27 AM

Find the global minimum to ten decimal places:

f(x,y) = esin(50x) + sin[60ey] + sin[70sin(x)] + sin[sin(80y)] - sin{10(x + y)] + 1/4(x2 + y2)


uuummm.....4?

Posted by: amish on January 12, 2005 10:32 AM

4 is correct, nice work

Posted by: johnnyH on January 12, 2005 10:34 AM

This problem has many variants. Of course the commonality is that you take two strings of calculation and then mix them together to create the illusion of a conflict.

Fun to think about though!

Posted by: TallDave on January 12, 2005 10:53 AM

yes commanalities are fun

Posted by: amish on January 12, 2005 10:57 AM

You wanna hear the puzzler about the three men in the sleazy Haitian hotel with only one hooker and only two condoms? How does every guy get his turn with the ($3) working girl without risk of STD?

Posted by: Pouncer on January 12, 2005 11:41 AM

I am simply disgusted at all this math. As a poli sci grad, I *hire* people to do my math.


http://members.fortunecity.com/wavjunky/swl-n/nomath.wav

Not so cheers,
Dave at Garfield Ridge

Posted by: Dave at Garfield Ridge on January 12, 2005 12:14 PM

You took log(2) to two different powers.

Is there a risk of STD if the men share condoms? Can you reuse condoms? Can the condom thats been put into the girl be re-used?

Guy A puts on both condoms. Does his thing. Guy B puts on condoms but takes off outer condom uses only first condom. Guy C puts on shared condom and flips the condom thats been taken off.

Guy A puts on both condoms. Does his thing. Guy B takes outer condom and puts on, with the area exposed to hooker on the outside. Guy C flips condom still on Guy A and puts on. Takes Guy B's condom and and puts on top of his condom.

Posted by: mike on January 12, 2005 12:22 PM

im never going to go on vacation with Mike and Pouncer. turn it in side out? my god man

Posted by: amish on January 12, 2005 12:27 PM
im never going to go on vacation with Mike and Pouncer
ROFL

I wish you guys could see the horrified look on my face when I read that too...

Posted by: fat kid on January 12, 2005 12:33 PM

In any case, Sobek chimed in on my little test thing - any of you other guys take it? I'd like to see how you math-heads do... Link is above a few posts...

Posted by: Fat Kid on January 12, 2005 12:39 PM

Who in the hell is Vinny Falcone? Other than in the Paul Anka "pep talk"? Oh Yea, My father first told me of the Bell Hop 30.00 puzzle around 40 years ago so it is very old and to me it is still a puzzle as long as you do not try and over work it with a pencil and paper. "That's just the Fuckin' way it is"

Posted by: Franco on January 21, 2005 08:36 AM
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