# Brain Teaser - A gang of 17 thieves steals a bag of gold coins



## 1SmartEngineer (May 11, 2009)

A gang of 17 thieves steals a bag of gold coins. In trying to share the coins equally, there are three coins remaining. In the ensuing fight over these three coins, one of the gang members is killed. In the next attempt to equally distribute the coins, there are 10 coins remaining. Again the gang fights, and another member dies. The third attempt is successful.

What is the smallest number of coins stolen?


----------



## RIP - VTEnviro (May 11, 2009)

Don't start threads in the Hall of Fame, n00b.

You've got to earn your way there, one Fudgey bathroom incident at a time.


----------



## jmbeck (May 11, 2009)

1SmartEngineer said:


> What is the smallest number of coins stolen?


Whoops.

Nevermind.


----------



## Dexman1349 (May 11, 2009)

I know the answer, but I used excel...


----------



## cement (May 11, 2009)

why does it take 17 thieves to steal one bag of coins?


----------



## Trashman (May 11, 2009)

must be very large bags, or very large coins


----------



## Sschell (May 11, 2009)

Ocean's 17?


----------



## MA_PE (May 11, 2009)

I used excel, too.


----------



## wilheldp_PE (May 11, 2009)

Trashman said:


> must be very large bags, or very large coins


It would have to be a very large bag of coins to hold the correct number. S'lotta coins.


----------



## benbo (May 11, 2009)

Trashman said:


> must be very large bags, or very large coins


If we're talking pennies or dimes, I don't think it's that big. But would seventeen pirates be willing to fight and kill over that amount? I doubt it.


----------



## humner (May 11, 2009)

17 thieves were required to steal the bag of coins because they were unionized, the number of coins is irrelevent due to the useless expendenture of union dues. The real question should have been, "How long does it take to have 17 thieves steal a bag of coins, disregarding seniority".


----------



## cement (May 11, 2009)

are there any holidays involved?


----------



## Master slacker (May 12, 2009)

Are they chocolate coins? If they are, is it too late to apply to be the 18 thief?


----------



## Capt Worley PE (May 12, 2009)

cement said:


> why does it take 17 thieves to steal one bag of coins?


The theft was run by gov contractors?


----------



## chaosiscash (May 12, 2009)

Capt Worley PE said:


> The theft was run by gov contractors?


Ouch.


----------



## MA_PE (May 12, 2009)

Trashman said:


> must be very large bags


We like large bags.


----------



## Dexman1349 (May 12, 2009)

^^^ Definately like large bags...


----------



## Chucktown PE (May 12, 2009)

I think testee likes large sacks.


----------



## dastuff (May 12, 2009)

It was a thief in the library with a candlestick!!!


----------



## Guest (May 12, 2009)

Wow .. just wow.

Where's the MS Paintbrush for this thread?

JR


----------



## frazil (May 12, 2009)

Can I get in on those gold coins?


----------



## Guest (May 12, 2009)

benbo said:


> If we're talking pennies or dimes, I don't think it's that big. But would seventeen pirates be willing to fight and kill over that amount? I doubt it.


See .. that's just it benbo ... it they were ninjas ... we wouldn't even be having this discussion!!! h34r:



humner said:


> 17 thieves were required to steal the bag of coins because they were unionized, the number of coins is irrelevent due to the useless expendenture of union dues. The real question should have been, "How long does it take to have 17 thieves steal a bag of coins, disregarding seniority".


Zing !!!



Capt Worley PE said:


> The theft was run by gov contractors?






chaosiscash said:


> Ouch.


Zing +1 !!!!

JR


----------



## wilheldp_PE (May 12, 2009)

This thread has gone long enough without an answer. I got

3930

, but it seems high to be the "minimum". Anybody confirm/deny?


----------



## benbo (May 12, 2009)

wilheldp_PE said:


> This thread has gone long enough without an answer. I got
> 
> 
> Spoiler
> ...





Spoiler



, but it seems high to be the "minimum". Anybody confirm/deny?


Confirm, at least that's what I got.


----------



## testee (May 12, 2009)

I'm just not that good with excel.

but what's this about sacks?


----------



## kevo_55 (May 12, 2009)

Wait, how did these thieves get the gold coins? Who has these gold coins?


----------



## Sschell (May 12, 2009)

correct.... but why did you decide to deviate from the theme of the thread and actually do calculations?!?


----------



## MA_PE (May 12, 2009)

wilheldp_PE said:


> This thread has gone long enough without an answer. I got
> 
> 
> Spoiler
> ...





Spoiler



, but it seems high to be the "minimum". Anybody confirm/deny?


Works for me.


----------



## MA_PE (May 12, 2009)

frazil said:


> Can I get in on those gold coins?


maybe if you have large bags.

sorry. i couldn't resist.


----------



## humner (May 12, 2009)

dude said:


> correct.... but why did you decide to deviate from the theme of the thread and actually do calculations?!?


I am expected to deviate, I work for the government, and yes, I am here to help.


----------



## Dexman1349 (May 12, 2009)

wilheldp_PE said:


> This thread has gone long enough without an answer. I got
> 3930


, but it seems high to be the "minimum". Anybody confirm/deny?


My answer as well


----------



## snickerd3 (May 12, 2009)

SapperPE said:


> I tried to do it in my head but then realized it would take me entirely too long to work that out at midnight, so I let it go and read the rest of the thread.


Much better plan!


----------



## OSUguy98 (May 12, 2009)

I got



Spoiler



360


, but I used Excel... did it quickly, didn't have time to double check formulas


----------



## wilheldp_PE (May 12, 2009)

OSUguy98 said:


> I got
> 360


, but I used Excel... did it quickly, didn't have time to double check formulas
That doesn't fulfill the 2nd condition of R10 after one thief dies.


----------



## cement (May 12, 2009)

more sig fig


----------



## cjdecuir (May 12, 2009)

cement said:


> more sig fig



Really easy, Got it in less than a minute, no Excel.


----------



## DVINNY (May 13, 2009)

humner said:


> ........, I work for the government, and yes, I am here to help.


oh crap. famous last words


----------



## IlPadrino (May 13, 2009)

Warning: Serious answer follows... if you were hoping for more "sack" responses, you'll be disappointed.

This is a classic "Chinese Remainder Theorem"...

The problem requires some n where:

n ≡ 3 (mod 17)

n ≡ 10 (mod 16)

n ≡ 0 (mod 15)

If you're not familiar with modulo notation, the first one says that some number n and 3 differ by 17... or in words we're taught in third grade, n divided by 17 has a remainder of 3.

OK... so the approach is to find some x, y, and z such that n = x + y + z with the following constraints:

x ≡ 3 (mod 17), which satisfies the first requirement and y and z are multiples of 17 (so adding them doesn't change the remainder)

y ≡ 10 (mod 16), which satisfies the second requirement and x and z are multiples of 16 (so adding them doesn't change the remainder)

z ≡ 0 (mod 15), which satisfies the third requirement and x and y are multiples of 15 (so adding them doesn't change the remainder)

And so this really means:

x ≡ 3 (mod 17) and x is a multiple of (15)(16) = 240

y ≡ 10 (mod 16) and y is a multiple of (15)(17) = 255

z ≡ 0 (mod 15)... and this is already satisfied by x and y being a multiple of 15, so we can forget about it!

OK then... let's find an x that works:

240 / 17 = 14 R2

480 / 17 = 28 R4

720 / 17 = 42 R6

960 / 17 = 56 R8

1200 / 17 = 70 R10

1440 / 17 = 84 R12

1680 / 17 = 98 R14

1920 / 17 = 112 R16

2160 / 17 = 127 R1 (126 R18)

2400 / 17 = 141 R3 (140 R20) &lt;---- this is the one!

And then let's find a y that works:

255 / 16 = 51 R15

510 / 16 = 31 R14

765 / 16 = 47 R13

1020 / 16 = 63 R12

1275 / 16 = 79 R11

1530 / 16 = 95 R10 &lt;---- this is the one!

So... n = 2400 + 1530 = 3930


----------



## OSUguy98 (May 13, 2009)

wilheldp_PE said:


> That doesn't fulfill the 2nd condition of R10 after one thief dies.


Yup... messed up a formula... had it referring to the wrong cell.....



Spoiler



3930


it is


----------



## MA_PE (May 13, 2009)

> ....or in words we're taught in third grade, n divided by 17


for the West Virginians that's "or in words we're taught in 8th grade 17 gozzinta n...."


----------



## benbo (May 13, 2009)

IlPadrino said:


> OK then... let's find an x that works:240 / 14 = 14 R2
> 
> 480 / 14 = 28 R4
> 
> ...


Why are you dividing by 14? Don't you mean 17?

Anyway, good explanation.


----------



## Flyer_PE (May 13, 2009)

MA_PE said:


> for the West Virginians that's "or in words we're taught in 8th grade 17 gozzinta n...."


Hey! I resemble that remark!

Actually, the math problems started out with: "How many gallons of 'shine will Pappy have to sell ..........."


----------



## IlPadrino (May 13, 2009)

benbo said:


> Why are you dividing by 14? Don't you mean 17?Anyway, good explanation.


Yup... I fixed it.


----------



## Capt Worley PE (May 13, 2009)

Flyer_PE said:


> Actually, the math problems started out with: "How many gallons of 'shine will Pappy have to sell ..........."


Or, "Cooter's pump shotgun holds five shells..."


----------



## dastuff (May 13, 2009)

IlPadrino said:


> Yup... I fixed it.


Sweet Chinese Answer! They must have had huge sacks back then!


----------



## Sschell (May 13, 2009)

some of us still do...


----------



## benbo (May 13, 2009)

IlPadrino said:


> Yup... I fixed it.


I would have thought the first person to throw down the "Chinese Remainder Theorem" would have been JR.


----------



## Guest (May 13, 2009)

benbo said:


> I would have thought the first person to throw down the "Chinese Remainder Theorem" would have been JR.


Unfortunately, I cannot jump in as quickly or as often as I used to with the new job. 

I am still developing algebraically whacked algorithms though! 

JR


----------



## 1SmartEngineer (May 14, 2009)

Thank you guys for passionately participating in my ice breaker. - 3930 is the correct answer.

I am Ken. A recently laid off engineer.

Glad to be here.


----------



## Sschell (May 14, 2009)

Sorry to hear that you got laid off ken. is your website a hobby or a potential source of income? (if that is not too personal of a question)


----------



## MA_PE (May 14, 2009)

OK ken. Time to post challenge No. 2


----------



## EM_PS (May 14, 2009)

MA_PE said:


> OK ken. Time to post challenge No. 2


^ I think he's got tons of them at his website. . .(http://www.engineeringdaily.net/) no sense making him do double duty - good luck Ken, btw

Here's some mathematical skullduggery for you:

2 = 1 how's this you say?

Let x=y

then x2=xy

and x2-y2=xy-y2

thus, (x+y)(x-y)=y(x-y)

so that (x+y)=y

therefore, x+x=x

and 2x=x

thus 2=1

[edit] sorry, forgot to include that this problem cannot be - why?


----------



## Sschell (May 14, 2009)

well... by that same logic:

x=y

1*(x-y)=1,000,000,000*(x-y)

thus 1=1,000,000,000...

which is much more dramatic.


----------



## EM_PS (May 14, 2009)

dude said:


> well... by that same logic:
> x=y
> 
> 1*(x-y)=1,000,000,000*(x-y)
> ...


you're simply saying 0=0, but you're on to it. . .


----------



## IlPadrino (May 14, 2009)

error_matrix said:


> ..
> 
> .
> 
> ...


Only if you're willing to say 0/0 = 1


----------



## EM_PS (May 14, 2009)

short lived teaser, esp w/ Sraymond around -



> thus, (x+y)(x-y)=y(x-y)so that (x+y)=y


algaebraically, this is permissible. . . EXCEPT division by zero is not

so this expression (x+y)(x-y)=y(x-y) cannot have the (x-y) terms cancel

ok, next teaser. . .


----------



## Capt Worley PE (May 14, 2009)




----------



## Sschell (May 14, 2009)

:appl: :appl: :appl:


----------



## IlPadrino (May 14, 2009)

How about this one... though maybe we've written about it before.

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

In other words, what are your odds of winning if you switch your choice?


----------



## Sschell (May 14, 2009)

^oh yeah... I remember that one... The answer really pissed me off, although I now believe it.


----------



## MA_PE (May 14, 2009)

^ It depends are you on a treadmill when you make the choice?


----------



## Capt Worley PE (May 14, 2009)

^And is the treadmill European (they're better)?


----------



## Wolverine (May 14, 2009)

IlPadrino said:


> In other words, what are your odds of winning if you switch your choice?


Hmm, let's see: at first you had a 33.33 chance that you guessed it right, but now you have better odds with a 50% chance so you should choose again.

Or else, you should not choose again since your first 33% chance multiplied again by taking a second 50% chance statistically yields only a 15% chance of being able to guess the right door.

Except that you really only had a 50% chance to start with, since you already had a 100% chance that Monty Hall was going to throw out one of the goat doors, so it doesn't matter which door you picked. Aw geez, where's my scotch bottle?

If anyone starts using the words "Airplane" and "Treadmill" in the same post following this, there's going to be a whupping. :chair:

Summon the :bann: :bash:


----------



## FLBuff PE (May 14, 2009)

Wolverine said:


> Hmm, let's see: at first you had a 33.33 chance that you guessed it right, but now you have better odds with a 50% chance so you should choose again.
> Or else, you should not choose again since your first 33% chance multiplied again by taking a second 50% chance statistically yields only a 15% chance of being able to guess the right door.
> 
> Except that you really only had a 50% chance to start with, since you already had a 100% chance that Monty Hall was going to throw out one of the goat doors, so it doesn't matter which door you picked. Aw geez, where's my scotch bottle?
> ...


Here's one for you...I got a really good deal on a *treadmill* on one of those online auction sites, but the owner didn't want to ship it, so I have to go pick it up. It is located 2,000 miles away. Should I use a car to pick it up or use an *airplane*? oking:


----------



## Sschell (May 14, 2009)

Instigators.... Mount up!


----------



## cement (May 14, 2009)

speaking of goats in car terms, would a standard model goat be a................

goatse?


----------



## Sschell (May 14, 2009)

thank god I never saw the goatSS or the goatex...


----------



## cement (May 14, 2009)

you could park a car there?


----------



## Capt Worley PE (May 15, 2009)

It better have a car cover.


----------



## IlPadrino (May 15, 2009)

Wolverine said:


> Hmm, let's see: at first you had a 33.33 chance that you guessed it right, but now you have better odds with a 50% chance so you should choose again.


Nope...



Wolverine said:


> Or else, you should not choose again since your first 33% chance multiplied again by taking a second 50% chance statistically yields only a 15% chance of being able to guess the right door.


Unh-uh... (wow... that's written an awful lot like uh-huh!)



Wolverine said:


> Except that you really only had a 50% chance to start with, since you already had a 100% chance that Monty Hall was going to throw out one of the goat doors, so it doesn't matter which door you picked. Aw geez, where's my scotch bottle?


No...


----------



## Dexman1349 (May 15, 2009)

IlPadrino said:


> How about this one... though maybe we've written about it before.
> Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
> 
> In other words, what are your odds of winning if you switch your choice?


2/3.

Your first choice had a 1/3 chance of getting the car, leaving a 2/3 chance of not getting it. Since the game show host shows you one goat door, the 2/3 chance is assigned to the remaining door.

Here are other explainations, all leaving a 2/3 chance:

http://mathforum.org/dr.math/faq/faq.monty.hall.html


----------



## Sschell (May 15, 2009)

ok.... so... how much wood could a wood chuck chuck if a wood chuck could chuck wood?


----------



## FLBuff PE (May 15, 2009)

dude said:


> ok.... so... how much wood could a wood chuck chuck if a wood chuck could chuck wood?


I think that the woodchuck could chuck as much wood as he wanted! By the way what is a wood chuck? Is it like a gopher? This is difficult to question answer. The amount of wood that woodchucks would chuck on a given day varies greatly with the individual woodchuck. According to a Wall Street Journal article, New York State wildlife expert Richard Thomas found that a woodchuck could chuck around 35 cubic feet of dirt in the course of digging a burrow. Thomas reasoned that if a woodchuck could chuck wood, he would chuck an amount equal to 700 pounds.

Some say it depends on three factors:

The woodchuck's desire to chuck said wood.

The woodchuck's need to chuck the aforementioned wood.

The woodchuck's ability to chuck the wood.

Others say:

He would chuck, he would, as much as he could, if a woodchuck could chuck wood.

If he could chuck wood, the woodchuck would chuck as much as he could!

A woodchuck would chuck as much wood as a woodchuck could chuck if a woodchuck could chuck wood.

A woodchuck would chuck all the wood that the woodchuck would chuck if a woodchuck could chuck wood.

If a woodchuck could chuck wood, he would and should chuck wood. But if woodchucks can't chuck wood, they shouldn't and wouldn't chuck wood. Though were I a woodchuck, and I chucked wood, I would chuck wood with the best woodchucks that chucked wood.

If a woodchuck could chuck wood, then s/he'd chuck all the wood, s/he'd chuck and chuck and chuck and chuck, if a woodchuck could chuck wood.

It would chuck the amount of wood that she sells seashells on the seashore divided by how many pickles Peter Piper picks.

One quarter of a sycamore if you give him a quarter for every quarter of the sycamore he cut.

It might depend on how many female woodchucks were present. Or, it could depend on whether the woodchuck's mother-in-law was around or not. If she was, he'd be chucking all day. If not, he'd be watching the football game.

Some maintain that woodchucks could not and would not chuck wood at all.

It depends on how good his dentures are!

A woodchuck, would chuck, as much wood, as a woodchuck, could chuck, If a woodchuck could chuck wood. But unfortunately, woodchucks do not chuck wood.

About 5.72 fluid litres of wood

About as many boards as the Mongol hoards would hoard if the Mongol hordes did hoard boards.

Um....... 23????

Tons. More than you can count. Honestly. No one can chuck more would than a woodchuck.

If the woodchucks name was Maurice, then it could chuck all the wood that it wants to. However, if its name is Frank, no chucking would be for it.

Due to the average size of a wood chuck and the general density of wood (not including cork) if a wood chuck could chuck wood it would probably get through about 6.573 pounds per day, assuming the wood chuck is functioning correctly.

Using the formula: (W + I) * C where W = the constant of wood, which is well known to be 61, as agreed in many scientific circles. I = the variable in this equation, and stands for the word "if" from the original problem. As there are three circumstances, with 0 equaling the chance that the woodchuck cannot chuck wood, 1 being the theory that the woodchuck can chuck wood but chooses not to, and 2 standing for the probability that the woodchuck can and will chuck wood, we clearly must choose 2 for use in this equation. C = the constant of Chuck Norris, whose presence in any problem involving the word chuck must be there, is well known to equal 1.1 of any known being, therefore the final part of this calculation is 1.1. As is clear, this appears to give the answer of (61 + 2) * 1.1 = (63) * 1.1 = 69.3. However, Chuck Norris' awesome roundhouse kick declares that all decimal points cannot be used in formulas such as this, and so it must be rounded to the final solution of 69 units of wood.

How Chuck Norris got involved

A woodchuck would only chuck as much would as Chuck Norris would allow it to, because the woodchuck shares Chuck's name. Therefore, Chuck must punish it and make it chuck as much wood as Chuck can. So, a woodchuck would chuck as much wood as Chuck could.

None cuz a wood chuck cant chuck wood! 

Approximately 3.9675 pounds every 5.6843 seconds. So there.

2.865 lbs every 11.3686 Seconds?

About 15 pounds a minute.

i speak differently i say WHAT DOES YOUR QUESTION HAVE TO DO WITH ANYTHING! and btw its 84% lol

it depends how good his dentures are!!!

As much as he needed to be satisfied

But the true jokey answer, as told by my grandfather is: As much wood as a woodchuck could chuck, if a woodchuck could chuck wood.

a woodchuck would chuck all the wood he could chuck if a woodchuck could chuck wood

Are you kidding? Everybody knows a woodchuck would chuck as much wood as a woodchuck could chuck if a woodchuck could chuck wood.

But it definitely couldn't chuck Chuck Norris.


----------



## Dexman1349 (May 15, 2009)

^^^ well played, sir. Well played.


----------



## FLBuff PE (May 15, 2009)

Dexman1349 said:


> ^^^ well played, sir. Well played.


Wish I could claim it as my own. Googled the question, and that was a post on Wikianswers. I had to post it, or Chuck Norris would kick my ass.


----------



## Sschell (May 15, 2009)

that made my brain hurt.


----------



## cement (May 15, 2009)

a woodchuck throws lots of dirt because it is in his interest to find food. to say that he would throw a similar weight of wood does not take motivational factors into account.


----------



## Sschell (May 15, 2009)

why are we "motivating" the woodchucks "wood"?


----------



## FLBuff PE (May 15, 2009)

dude said:


> that made my brain hurt.


It's your own fault...you asked.



cement said:


> a woodchuck throws lots of dirt because it is in his interest to find food. to say that he would throw a similar weight of wood does not take motivational factors into account.


The woodchuck could concievably be chucking wood to make his home.



dude said:


> why are we "motivating" the woodchucks "wood"?


Again, you're the sicko that asked.


----------

