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rmac22
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Posted on Sun, Feb 10, 2013 16:24

Puzzle #3

 

 

Suppose you have an unlimited supply of fuses that burn at non-uniform rates, but each fuse is exactly the length necessary to burn for one hour. 

 

How would you accomplice using one or more of them to time 45 minutes?

 

Hint one:  First accomplice figuring out how to time 30 minutes.  Then accomplice figuring out how to time 1 hour and 30 minutes.  At that point you should be able to figure out how to time 45 minutes. 

 

Hint two:   Either presume you can move instantaneously or ignore the slight errors because you can’t.

 

Hint three:  Wear fireman’s gloves -- just kidding. 

 

RMac



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rmac22
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Posted on Tue, Feb 26, 2013 21:37

Dakota -- I don’t know.  Timing the market is tricky.  I only managed to do it once.  Did well that time though.

 

RMac 

 



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Dakota35
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Posted on Mon, Feb 25, 2013 20:18

Quoting rmac22:

Dakota – Well, I really can’t make my mind hook into the stock market stuff, short term, long term, you name it.  Not the way my mind seems to work.   Thanks for the postings.

 

 

Windrider – In the future, I will happily leave all blasting of stumps or rocks, to you and / or any experts you choose to employ.   Ditto on pulling said items out of the ground with chains and caterpillars.    

 

Still don’t know why you thought any real life handbook or expert on fuses would help on a puzzle that was deliberately designed so that such would not apply.

 

Anyhow, it has been fun.  Thanks for the postings.

 

 

Hope – Compliment and complement still give me a bit of trouble.  Nice to hear from you.

 

 

RMac



Well rmac22, I'm the  biggest fool on this site.  You can look at my prediction and see that I was correct.  I could have made $16000 in 4 days but I waited and then my brokerage house didn't get a buy for me despite the investment dropping below what my limit order.  I'm really hating myself right now.



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rmac22
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Posted on Mon, Feb 18, 2013 10:20

Dakota – Well, I really can’t make my mind hook into the stock market stuff, short term, long term, you name it.  Not the way my mind seems to work.   Thanks for the postings.

 

 

Windrider – In the future, I will happily leave all blasting of stumps or rocks, to you and / or any experts you choose to employ.   Ditto on pulling said items out of the ground with chains and caterpillars.    

 

Still don’t know why you thought any real life handbook or expert on fuses would help on a puzzle that was deliberately designed so that such would not apply.

 

Anyhow, it has been fun.  Thanks for the postings.

 

 

Hope – Compliment and complement still give me a bit of trouble.  Nice to hear from you.

 

 

RMac



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Windrider735
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Posted on Sun, Feb 17, 2013 04:50

Rmac...

 

The area I live in has more than it's share of trees and rocks. When I first moved here a lot of both were blasted, but my own preference is to dig them out with a tractor, backhoe, or cat and chains...mainly because I'm rather lazy and don't care to have to pick blasted rock out of a just-cleared field. I have a friend who has a license to blast, and I would never attempt it without having been taught by an expert. Don't have any limbs to spare and I don't take foolish chances...life's too short as it is.

 

What I failed to add was that the same test would have to be done on all the different fuses and then apply the math, but thought most readers would assume that. The testing of the fuses themselves has little to do with the blasting caps in this equation. An experienced expert in that field would know which ones to use with what job.



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Dakota35
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Posted on Sun, Feb 17, 2013 02:43

Quoting rmac22:

If only I could do that.  Mathematics and Logic behave.  The stock market does not behave.   Richard Wiseman, a psychologist, has compared the predictions of the respected Market Gurus with those of a grandmothers group and a child of about six (I think).  This is all from memory, which sometimes fails me so don’t hold me to exact accuracy.  The overall results are what I remember.  I did my best to recreate the sense and spirit of the story

 

I don’t remember the time span he used, but the Child beat everyone, the grandmothers came in next, and the experts a distant third. 

 

 

RMac

 



For me, I like to try to predict the behavior of investors based on future events.  I watched as the "fiscal cliff" issue caused the VIX (I'll be playing the VIX) to rise for a few days until the crooks in Washington patched the infinitely deep hole their digging.  Then the markets once again continued on their upward path.  It's a game of musical chairs, as all on WallStreet know ultimately the music will stop, just don't be the last one standing.  So with the up coming sequester,  in which neither Dems or Rep. have made much mention, one has to wonder the impact on the markets.  My thoughts is that there will be one of two scenarios.  Either both sides will bicker up until the last moment causing a pull back in the markets or they will allow the sequester to take effect only addressing it after seeing the damage...based on the severity of the damage.  Either scenario should cause a pull back in the markets.  I just can't imagine how people can ignore 110 billion dollars being removed from the economy each year for ten years as not damaging.  Of course considering the Fed is pumping so much money into the economy maybe people see that as counter acting.  But my play is on traders emotions for short term gains.  I know the pull back is going to happen, I'm just not sure if I have it timed properly.  But my risk -vs- reward seem rather well founded.  Time will tell.  There are events in the market which are easily predictable.  I've made some really good money.  The key is to wait for what I call a "giveme" or a almost sure thing.  Natural gas was a "giveme" not long ago...and at some point will be again both long and short term...thanks to fracking and future export.  Oh, and I can show you a virtually guaranteed investment...created by the big boys to scam the small fish.



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rmac22
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Posted on Sat, Feb 16, 2013 10:13

Quoting Dakota35:

Yes, I knew it could be extended to some degree but didn't think it out like you listed.  Things like that, can make me a little nuts.

 

Now if you can just tell me when the S&P 500 is going to tank, I would be your best friend.  I'm thinking of placing a short bet that the sequester will have a near term negative effect then a bounce followed by again down on the debt ceiling.  I try to stack the odds in my favor but the markets are insane and for the most part unpredictable.  Wish me luck and I'll only tell if I was correct. :)  I may miss the move all together as I'm waiting until the last possible moment because the trading instrument is so volatile.



If only I could do that.  Mathematics and Logic behave.  The stock market does not behave.   Richard Wiseman, a psychologist, has compared the predictions of the respected Market Gurus with those of a grandmothers group and a child of about six (I think).  This is all from memory, which sometimes fails me so don’t hold me to exact accuracy.  The overall results are what I remember.  I did my best to recreate the sense and spirit of the story

 

I don’t remember the time span he used, but the Child beat everyone, the grandmothers came in next, and the experts a distant third. 

 

 

RMac

 



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Dakota35
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Posted on Fri, Feb 15, 2013 22:32

Quoting Hoping4Love2000:

What I love about RMAC....

When he isn't blowing things up... 

He knows TOO, TO and TWO... ;) 



Like I said, he's smarter than I...or is it me?



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Hoping4Love2000
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Posted on Fri, Feb 15, 2013 21:21

What I love about RMAC....

When he isn't blowing things up... 

He knows TOO, TO and TWO... ;) 



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Dakota35
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Posted on Fri, Feb 15, 2013 01:22

Quoting rmac22:

Dakota – Speaking of interesting.  You can extend puzzle #2 to 9 marbles and still solve it in at most 2 weighings with the balance.   You already know how.  Then you can extend it to 27 and solve it with at most  3 weighings with the balance.  And you can extend it to 81 and solve it with at most 4 weighngs with the balance. 

 

So

 

3 marbles 1 weighing

9 marbles 2 weighings

27 marbles 3 weighings

81 marbles 4 weighings

 

Interesting pattern!!!

 

2 through 3 both require at most 1

4 through 9 all require at most 2

10 through 27 all require at most 3

28 through 81 all require at most 4

 

It is bit busy to establish all of that though.

 

RMac



Yes, I knew it could be extended to some degree but didn't think it out like you listed.  Things like that, can make me a little nuts.

 

Now if you can just tell me when the S&P 500 is going to tank, I would be your best friend.  I'm thinking of placing a short bet that the sequester will have a near term negative effect then a bounce followed by again down on the debt ceiling.  I try to stack the odds in my favor but the markets are insane and for the most part unpredictable.  Wish me luck and I'll only tell if I was correct. :)  I may miss the move all together as I'm waiting until the last possible moment because the trading instrument is so volatile.



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rmac22
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Posted on Thu, Feb 14, 2013 18:07

Dakota – Speaking of interesting.  You can extend puzzle #2 to 9 marbles and still solve it in at most 2 weighings with the balance.   You already know how.  Then you can extend it to 27 and solve it with at most  3 weighings with the balance.  And you can extend it to 81 and solve it with at most 4 weighngs with the balance. 

 

So

 

3 marbles 1 weighing

9 marbles 2 weighings

27 marbles 3 weighings

81 marbles 4 weighings

 

Interesting pattern!!!

 

2 through 3 both require at most 1

4 through 9 all require at most 2

10 through 27 all require at most 3

28 through 81 all require at most 4

 

It is bit busy to establish all of that though.

 

RMac



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rmac22
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Posted on Thu, Feb 14, 2013 18:05

Windrider – associating this puzzle with anything to do with blasting rocks or stumps could get you killed.

 

 I spent half a summer once blasting stumps.  Various sized stumps.  Fuses, caps, and dynamite.  Every once in a while got too much dynamite under a stump.  Maybe three times for the summer.  A little too much was ok.  Just right was ok also, but risked using too little.  Too little would result in all the dirt being blown out from under the stump.  Then you had to cut all the roots and pull it out with chains and the truck.  Waste a lot of time doing that.  So you tended to error on the side of just a wee bit too much.

 

However, way too much sent the stump way over the top of the trees.  The only safe place when that happened was under the truck. 

 

 

Dakota – Smarter, I don’t know.  I’ll accept the compliment though. 

 

 

RMac



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Windrider735
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Posted on Wed, Feb 13, 2013 21:23

Is this an 'open book' test? If so...then here's your answer.   A test burn is (usually) a fairly easy thing to do, and can aid a blaster in getting his/her charge to go off within one second of when that explosion is desired. To begin with, s/he cuts 3 feet of fuse from the roll s/he plans to use when setting off the charge. Then, s/he carries this fuse (along with a mechanical match) to a setting that’s as similar to the location where the charge will be placed, as possible. If the charge is going to be used to blow down a train trestle that runs across a mountain pass high in the sky, then the blaster needs to take that test fuse up a mountain to the same elevation. If the charge is going to be set 300 feet below the ocean, the blaster needs to don a wet suit and air tanks, and take it down beneath the waves – preferably to 300 feet of depth.

Once the blaster has gotten as close as possible to the expected conditions, s/he then pulls out a stop watch, hooks up the Mechanical Match, and sets off the Time Fuse. The blaster times how long it takes, from the moment the Mechanical Match is fired, until that little spurt of flame shoots out the other end of the fuse.

Now, the blaster takes that number (the length of time it took to burn three feet) and divides it by 3 (the number of feet it burned in that time). The answer tells the blaster what this specific Time Fuse’s burn rate will be under those conditions.

If, for example, it somehow took 3 minutes to burn three feet, the blaster would divide the 3 minutes (time it took to burn) by the 3 feet (the length of the fuse tested) and arrive at a burn rate of 1 minute per foot. Since s/he now knows that this fuse will burn at the rate of 1 min./ft, if the blaster wants a 6-minute fuse, s/he will divide those 6 minutes by the burn rate. 6 mins. ÷ 1 min./ ft. = 6 feet of Time Fuse. In other words, s/he now knows to cut off six feet of Time Fuse, if s/he wants the fuse to burn for six minutes before the explosion occurs.

In reality, our blaster is much more likely to get a number like “1 minute and 18 seconds”, or “1 minute and 42 seconds” when s/he does the three-foot test burn. The easy way to handle this is to convert minutes to seconds and add it to the seconds left over. (For example, if our time was 1 minute and 42 seconds, we'd convert our 1 minute to 60 seconds, then add that to 42 seconds. 60 + 42 = 102. So, now we know it takes 102 seconds for the fuse to burn 3 feet. Dividing 102 seconds [the time] by 3 feet [the distance burned] gives us a burn rate of 34 seconds per foot.)

In the example above, if we wanted a 6-minute fuse on our charge, we'd divide 6 minutes (which is the same as 6 x 60 = 360 seconds) by 34 seconds/foot.

360 seconds ÷ 34 seconds/foot = 10.5882 feet. But, what about the .5882 feet?

Well, now we multiply 0.5882 x 12 to get inches. 0.5882 x 12 = 7.0584 inches. So, now we have a fuse that’s 10 feet and 7.0584 inches long.

But … what about the .0584 inches?

Simply multiply 0.0584 x 16 to get sixteenths of an inch. 0.0584 x 16 = 0.9344

0.9 can be rounded up to 1, so … we're going to measure out 10 feet and 7 & 1/16 inches of Time Fuse, then we're going to cut off that hunk that’s 10 feet and 7 & 1/16 inches long.
  Credit for this information goes to  "Sleuth Sayers" and Dixon Hill...for an interesting and informative lesson on blasting. Your site rocks!


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Dakota35
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Posted on Wed, Feb 13, 2013 00:43

Rmac, just checked out your profile...I Knew it!  You are smarter me.  :)  Your puzzles are interesting.



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Dakota35
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Posted on Wed, Feb 13, 2013 00:35

Quoting rmac22:

Dakota:  Since the fuses do not burn uniformly, one cannot know when 15 minutes is up just using the fuses.   At least not with just one fuse at a time.  If it is even possible to get 15 minutes using multiple non uniform burning fuses I do not know how.

 

One can get 30 minutes by lighting the first fuse at each end.  Where the “flames” meet has to be 30 minutes.

 

Have the second  fuse ready to meet where  the “flames” meet on the one above.  Since you don’t know where that will be you have to presume you can move instantaneously.   This will give you 1 hour and 30 minutes. 

 

If you had stated both ends of the first fuse and one end of the second, the second one would have burned down to only 30 minutes left when its other end is ignited by instantaneously touching it to the point where the flames meet  on the first fuse.   So now you have effectively a 30 minute fuse burning at both ends.  Thus you will get an additional 15 minutes plus the 30 minutes from the first fuse.  Done.

 

This is the last puzzle I plan on posting.   At least for now.   

 

If you enjoy this sort of thing, you might try the Mensa practice quizzes.  Otherwise try some of the purported Google interview questions on the internet.

 

Thanks for your participation.

 

RMac

 



I've never been good at word problems.  I just thought about it quickly and you said; "each fuse is exactly the length necessary to burn for one hour" 1 hour is 1 hour no matter the length of the fuse and " How would you accomplice using one or more of them to time 45 minutes?"  So I just assumed that if all fuses were timed for 1 hour then allowing a fuse to burn for 15 min then extinguishing would leave 45 min. no matter the burn rate at any point in the fuse, the fuse is still 1 hour.  I was just going to use a watch, time for 15 min. and extinguish the fuse.  But I suppose a watch is not allowed.  I must of totally missed this one. :)  Next time, I'm going to use a dynamite cap instead...those darn fuses are going to get me killed.

I failed college math (not all classes) for 2 reasons.  1. the professors said that I may have gotten the correct answer but I didn't follow the correct procedures for getting it.  2.  You'd think when he said he wouldn't take up notebooks at the beginning of the semester that he wouldn't...(so, there was no work done in my notebook)....well he did and it was a huge part of the grade (something like 60%).  I made a D in the class.   I'm still angry about it after all these years. :)  Now I'm a idiot at math all because of that guy. :)  

 

 



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rmac22
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Posted on Tue, Feb 12, 2013 08:29

Dakota:  Since the fuses do not burn uniformly, one cannot know when 15 minutes is up just using the fuses.   At least not with just one fuse at a time.  If it is even possible to get 15 minutes using multiple non uniform burning fuses I do not know how.

 

One can get 30 minutes by lighting the first fuse at each end.  Where the “flames” meet has to be 30 minutes.

 

Have the second  fuse ready to meet where  the “flames” meet on the one above.  Since you don’t know where that will be you have to presume you can move instantaneously.   This will give you 1 hour and 30 minutes. 

 

If you had stated both ends of the first fuse and one end of the second, the second one would have burned down to only 30 minutes left when its other end is ignited by instantaneously touching it to the point where the flames meet  on the first fuse.   So now you have effectively a 30 minute fuse burning at both ends.  Thus you will get an additional 15 minutes plus the 30 minutes from the first fuse.  Done.

 

This is the last puzzle I plan on posting.   At least for now.   

 

If you enjoy this sort of thing, you might try the Mensa practice quizzes.  Otherwise try some of the purported Google interview questions on the internet.

 

Thanks for your participation.

 

RMac

 



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rmac22
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Posted on Mon, Feb 11, 2013 11:45

Hope, the premise is that you only get to use the fuses to determine the time interval.  It is always nice hearing from you.

 

RMac

 

 



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Dakota35
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Posted on Sun, Feb 10, 2013 22:33

My brain got screwed from the very start as I was thinking electrical fuse.  Yeah, just over-load it at 45 min. LOL  I've got to stop trying to figure these out, my brain just gets tied in knots.  rmac your brain must work much better than mine, I'll just bow to you and pass on this one. Quick guess. Just burn 15 min. of each fuse and put it out, then you'll have 45 min. left.



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Hoping4Love2000
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Posted on Sun, Feb 10, 2013 20:56

In Atlanta, they have a restaurant called the SUN DIAL. It is a moving floor.. (Really cool!) 

 

You end up at the same spot in an hour!

 

If I was going to get to my original seating position BEFORE the hour, they would have to "speed up" the process of the floor moving. 

 

Same premise here. You have to speed the process up. If they all burn for an hour, regardless of length... "size" doesn't matter! LOL... (So they should all have same equation) 

 

My guess would be to light other end after 15 minutes, so it burns quicker than 1 hour? 

 

However, my math skills are not very talented.. So I am just guessing since we are using half hour and hour intervals. Does that make sense? 

 

I don't think you could "alter" the fuse, (acceleraters etc) because THEY ARE UNPREDICTABLE, so you have to work with what you have only? 

 

Night RMAC! I'm turning back into a pumpkin!! ;) 



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