bonanova Posted August 17, 2009 Report Share Posted August 17, 2009 (edited) For reasons known only to yourself, you want to eat a really hard-boiled egg. You decide that a nine-minute boil will suffice. If only you had a timer! As luck would have it a weird peddler happens by. For the incredibly low price of $0.39, offers you an inexhaustible supply of 4-minute and 7-minute fuses. The fuses are guaranteed to burn at a constant rate of speed. You go to the kitchen and bring a pot of water to a rapid boil. What is the shortest elapsed time before you can eat your guaranteed 9-minute egg? Edit: see post #3. Edited August 17, 2009 by bonanova Change fuse to hourglass. Thanks to Gmaster. Quote Link to comment Share on other sites More sharing options...
0 Gmaster479 Posted August 17, 2009 Report Share Posted August 17, 2009 If they burn at a constant speed, then start the 7 minute fuse. When that is all gone, then burn the 4 minute fuse in half and at both ends. They'll meet each other in 2 minutes. 7+2=9. Bonanova, is this really this simple or is this a really complicated puzzle? Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted August 17, 2009 Author Report Share Posted August 17, 2009 If they burn at a constant speed, then start the 7 minute fuse. When that is all gone, then burn the 4 minute fuse in half and at both ends. They'll meet each other in 2 minutes. 7+2=9. Bonanova, is this really this simple or is this a really complicated puzzle? Shot myself in the foot adding a twist to an hourglass problem. OK you got me ... they aren't fuses, they're hourglasses. Solve it using two hourglasses - 4 and 7 minutes respectively. Nice catch! Quote Link to comment Share on other sites More sharing options...
0 Gmaster479 Posted August 17, 2009 Report Share Posted August 17, 2009 ummm thanks. I think. Now I have to actually think... Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 17, 2009 Report Share Posted August 17, 2009 (edited) Oh dear. I think I've got it, but I may be making it more complicated that it's supposed to be. Start them at the same time. Once the 4 is done (4 minutes), flip it over immediately. When the 7 finishes (3 more minutes, total of 7 minutes), flip it immediately. When the 4 finishes (one more minute, total of 8), flip the 7 again. When that finishes (one more minute), you've got 9 minutes. I hope that makes sense. Or On the other hand, since the question asks for the "shortest elapsed time", that will simply by 9 minutes, regardless of how you flip hourglasses. Edited August 17, 2009 by AnapesticTetrameter Quote Link to comment Share on other sites More sharing options...
0 Gmaster479 Posted August 17, 2009 Report Share Posted August 17, 2009 yea that is the smart aleck answer. I think bonanova was trying to make us think it was harder then it actually was. But yea i've seen this problem before and you got it Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 17, 2009 Report Share Posted August 17, 2009 16 minutes: 7 minute fuse (begin concurrently with 4 minute followed by another 4 minute -- the 4+4 overrun the 7 by 1 minute) begin boiling as the 7 minute fuse (minuteglass) runs out. begin third 4 minute fuse at end of the second 4 minute fuse then fourth and final 4 minute fuse 4+4+4+4=16 4+4-7+4+4-->1 minute + 4 minute + 4 minute = 9 minutes Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 17, 2009 Report Share Posted August 17, 2009 16 minutes: 7 minute fuse (begin concurrently with 4 minute followed by another 4 minute -- the 4+4 overrun the 7 by 1 minute) begin boiling as the 7 minute fuse (minuteglass) runs out. begin third 4 minute fuse at end of the second 4 minute fuse then fourth and final 4 minute fuse 4+4+4+4=16 4+4-7+4+4-->1 minute + 4 minute + 4 minute = 9 minutes Regarding the fuses, one only needs to light the 7 min, wait for it to burn, then light the 4 min at both ends. That would be 9 minutes. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 17, 2009 Report Share Posted August 17, 2009 Place the seven minute timer in the water with the egs and mark the level of the water as boiling commences, whilst at the same time, turning the 4 minute timer over. After 4 minutes, again note the level of the water on the sven minute timer and turn the 4 minute timer over. during this second leisurely 4 minutes, calculate using finger widths how much water has evaporated in the first four minutes(by measuring between water level marks on the 7 minute timer). All things remaining equal, the water should evaporate at the same rate, so you'll then be able to calculate the water level after 9 minutes and mark it on the seven minute timer. Pop the 7 minute timer back in the water and wait for the water to reach that level. The second 4 minute tiiming session is purely there so you know that you've done your calculations in time! (in fact, you'll have a minute up your sleeve)) Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted August 17, 2009 Author Report Share Posted August 17, 2009 Oh dear. I think I've got it, but I may be making it more complicated that it's supposed to be. Start them at the same time. Once the 4 is done (4 minutes), flip it over immediately. When the 7 finishes (3 more minutes, total of 7 minutes), flip it immediately. When the 4 finishes (one more minute, total of 8), flip the 7 again. When that finishes (one more minute), you've got 9 minutes. I hope that makes sense. Or On the other hand, since the question asks for the "shortest elapsed time", that will simply by 9 minutes, regardless of how you flip hourglasses. First answer has it. Congrats. Smart alek fails because the 9 minutes is not guaranteed, as required. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 17, 2009 Report Share Posted August 17, 2009 It ia neat answer, but I had to look up what "anapestic" meant! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 17, 2009 Report Share Posted August 17, 2009 1, seven min fuse 4, eight min 17 minutues till a guarenteed 9 min egg i think i got it Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 17, 2009 Report Share Posted August 17, 2009 1, seven min fuse 4, eight min 17 minutues till a guarenteed 9 min egg i think i got it perfect answer for hourglasses i wouldn't have gotten it regarding the fuses, do they burn at a constant rate, maybe, maybe not a four minute fuse could burn 1/2 way for the first 3 min and 1/2 way the last min. how do you flip fuses? if you burned off a min how could you flip it to measure a precise minute Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 17, 2009 Report Share Posted August 17, 2009 First answer has it. Congrats. Smart alek fails because the 9 minutes is not guaranteed, as required. perfect answer for hourglasses i wouldn't have gotten it regarding the fuses, do they burn at a constant rate, maybe, maybe not a four minute fuse could burn 1/2 way for the first 3 min and 1/2 way the last min. how do you flip fuses? if you burned off a min how could you flip it to measure a precise minute Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted August 17, 2009 Author Report Share Posted August 17, 2009 how do you flip fuses? if you burned off a min how could you flip it to measure a precise minute That's the twist I intended to add. Can you see how? You must assume they burn at a constant rate. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 17, 2009 Report Share Posted August 17, 2009 (edited) You'd have to wait 7 minutes to cook an egg for 9 minutes straight with these fuses. But since I'm not sure if we're supposed to use power fuses or fuses for TNT not sure if it would take 2 or 5 fuses to solve. My math: 7-4=3 4-3=1 1+4+4=9 Edited August 17, 2009 by AuBug Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 17, 2009 Report Share Posted August 17, 2009 perfect answer for hourglasses i wouldn't have gotten it regarding the fuses, do they burn at a constant rate, maybe, maybe not a four minute fuse could burn 1/2 way for the first 3 min and 1/2 way the last min. how do you flip fuses? if you burned off a min how could you flip it to measure a precise minute There are two types of fuses in the world there are the kind you use to ignite black powder and other explosives. Then there is the type that are used in house to give the home protection from burning down when there is a surge. The ones used in a house flip off a circuit so that a house doesn't burn down. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted August 17, 2009 Author Report Share Posted August 17, 2009 There are two types of fuses in the world there are the kind you use to ignite black powder and other explosives. Then there is the type that are used in house to give the home protection from burning down when there is a surge. The ones used in a house flip off a circuit so that a house doesn't burn down. For your solution, you shouldn't have to wait at all be begin cooking. Power fuses wouldn't be rated in minutes, rather in Amperes. That should avoid any confusion. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 17, 2009 Report Share Posted August 17, 2009 OK, if it's hourglasses, then I agree that Anapestic has it correct, but for the original riddle, I think it has to be 16 as the shortest *for sure* time as Santiago said. Gmaster's idea, while logically sound, it not sound it practice because it assumes that the fuse burns at a constant rate -- which it doesn't. Most fuse burns at a wildly inconsistent rate, so a fuse lit at both ends will rarely end up meeting directly in the middle... Given the parameters of the puzzle, 16 mins is the shortest time you can be sure of... Furthermore, isn't it against the very nature of a logic puzzle to "assume" anything? If it isn't stated, then for the purpose of the puzzle, it doesn't exist. Otherwise there might be any number of answers, like, "well, I assume that I can use my stopwatch, since I always have one in my pocket..." Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 17, 2009 Report Share Posted August 17, 2009 0 MIN: Start a 4 and a 7. 4 MIN: When the 4 is done start another 4 7 MIN: When the 7 is done start the egg. 8 MIN: Egg 1 MIN: When the 2nd 4 is done start another 4. 12 MIN: Egg 5 MIN: When the 3rd 4 is done start another 4. 16 MIN: Egg 9 MIN: Done. Quote Link to comment Share on other sites More sharing options...
0 Gmaster479 Posted August 17, 2009 Report Share Posted August 17, 2009 OK, if it's hourglasses, then I agree that Anapestic has it correct, but for the original riddle, I think it has to be 16 as the shortest *for sure* time as Santiago said. Gmaster's idea, while logically sound, it not sound it practice because it assumes that the fuse burns at a constant rate -- which it doesn't. Most fuse burns at a wildly inconsistent rate, so a fuse lit at both ends will rarely end up meeting directly in the middle... Given the parameters of the puzzle, 16 mins is the shortest time you can be sure of... Furthermore, isn't it against the very nature of a logic puzzle to "assume" anything? If it isn't stated, then for the purpose of the puzzle, it doesn't exist. Otherwise there might be any number of answers, like, "well, I assume that I can use my stopwatch, since I always have one in my pocket..." I get what your are saying. 16 minutes is correct assuming the fuses don't burn at a constant speed. I simply followed the parameters of the original puzzle where it stated that they burned at a constant speed to get my answer. I understand that the 16 minute answer is what bonanova was probably looking for as he tried to put a twist on this classic problem, but that's what I get for reading directions. Good job everyone Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 17, 2009 Report Share Posted August 17, 2009 It takes 16 minutes: First start a 7 and 4 minute hourglass at the same time. After the 4 minute hourglass ends, start another 4 minute hourglass. After the 7 minute hourglass ends, put your egg in the water. After the 4 minute hourglass ends a minute later, start a 4 minute hourglass and after that ends (egg in water 5 minutes), start another 4 minute hourglass. After the last hourglass ends, take your egg (which has been boiling for nine minutes) out of the water, 16 minutes after you started the process. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted August 17, 2009 Author Report Share Posted August 17, 2009 has a nine-minute hourglass solution. The OP uses the word form guarantee twice: once for the uniform fuse burn, once for the boil time. Within those stated parameters, the boil time only has to be as certain as the rate of burn of the fuses. Given that, and AT's solution [and arbitrarily ruling out lighting any one fuse in two places] is there a nine-minute fuse solution? Specifically, can fuses emulate AT's solution? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 17, 2009 Report Share Posted August 17, 2009 Given that the fuse does burn uniformly, then the answer is yes. Just line up two four minute fuses and light one end of one and the opposite end of the other. When the burning parts pass each other light your 7 minute fuse. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 17, 2009 Report Share Posted August 17, 2009 Given that the fuse does burn uniformly, then the answer is yes. Just line up two four minute fuses and light one end of one and the opposite end of the other. When the burning parts pass each other light your 7 minute fuse. But dismissed it as potentially being too inexact. In addition, the puzzle doesn't say (while it implies such) that all 4 minute fuses are the same length. In other words, you could have 5 four minute fuses, each with different burn rates and of lengths sufficient to give you exactly 4 minute burns. I've been treating the fuses as either a 4 minute or 7 minute "black box". I.e. You press a button on the box and either 4 minutes or 7 minutes later (depending on the box; you know which is which), it "dings." However, I've been treating them as if you can't see the workings, so the only thing you know is the instant you press the button and the instant the ding occurs. Probably wrong in the context of a "constant burn rate" fuse. Treating it thusly, the 7 minute to 16 minute solution is the only one that works (since in my interpretation, the only reliable times you can get are after 4,7,8,11,12,14,15,16,18,19...And the first difference of 9 is between the 7th and 16th minutes. Or, if you allow taking the egg out, you can do it in 14 minutes Light a 4 minute and 7 minute fuse. Put the egg in when the four minute fuse goes off; and light a second 4 minute fuse Take the egg out when the first 7 minute fuse goes off (three minutes elapsed from previous step). Light a second 7 minute fuse. Put the egg back in when the second four minute fuse goes off (1 minute elapsed from previous step) Take the egg out when the second 7 minute fuse goes off. (6 minutes elapsed from previous step) Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted August 18, 2009 Author Report Share Posted August 18, 2009 Given that the fuse does burn uniformly, then the answer is yes. Just line up two four minute fuses and light one end of one and the opposite end of the other. When the burning parts pass each other light your 7 minute fuse. I'll allow the interpretation that would make this solution work: Equal time fuses are also equal length, and burn rate - inches per second, say, all the same and constant. Still, there's a method that emulates the hourglass solution given above with no waiting time. Fold a 4-minute fuse in half and touch the fold point to a 7-minute fuse.You get a 2-minute burn from the 4-minute fuse while lighting it at only one point. OK, now what's the hourglass solution implemented by fuses? Quote Link to comment Share on other sites More sharing options...
Question
bonanova
For reasons known only to yourself, you want to eat a really hard-boiled egg.
You decide that a nine-minute boil will suffice.
If only you had a timer!
As luck would have it a weird peddler happens by.
For the incredibly low price of $0.39, offers you an inexhaustible supply of 4-minute and 7-minute fuses.
The fuses are guaranteed to burn at a constant rate of speed.
You go to the kitchen and bring a pot of water to a rapid boil.
What is the shortest elapsed time before you can eat your guaranteed 9-minute egg?
Edit: see post #3.
Edited by bonanovaChange fuse to hourglass. Thanks to Gmaster.
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