Interview Riddle - 16 Bikes || Logic and Optimization Puzzle
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- Опубліковано 28 вер 2024
- Interview puzzle :
There are 16 motorbikes with a tank that has the capacity to go 100 km (when the tank is full).
Using these 16 motorbikes, what is the maximum distance that you can go?
-All the motorbikes are initially fully fuelled.
-They all start from the same point.
-and Each bike has a rider on it.
Pls Note: We just have to find out the maximum distance that we can go, We don't want all the bikes to reach at that final point.
It's not a hard riddle, however, it requires a brain twisting trick to solve this problem correctly.
So, Pause the video and think logically.
It's an amazing Google interview riddle to challenge your intelligence.
So if you are looking for a job at Google, please study optimization based puzzles in detail.
You can share puzzles and riddles with me on these links:
Gmail : logicreloaded@gmail.com
Facebook(message) : / mohammmedammar
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Is it only me who thought attaching bikes with the ropes, a perfect indian solution
There are no ropes in the problem.
@@literallylegendary6594 😂there are no pipes and funnels too in the problem to transfer fuel.
Exactly! And even assuming each bike can only tow one other, you still get 500km!
@@literallylegendary6594 there may not have been rope, but each bike has it's own rider.. just make it their responsibility to hold on to the bike in front of them ;)
Me too
The maximum distance that can be covered is 1600 km. The riddle does not say 'what is the furthest you can get from the start'. It says 'what's the maximum distance? '
*alll bikes start from the same point, is part of the conditions
@@OscarLT321 on a 100km circular track a bike will run out of fuel back at the start, at which point I get off my empty bike and get on a full one and continue. After I've used all the bikes I have traveled 1600 km and not broken any of the conditions.
@@pintokitkat With that logic you could also say it's way beyond 1600 km if you can refuel after each lap. There are millions of loopholes to get out of solving an equation
@@OscarLT321 what he says is perfectly logical and you come around the corner and compare it to refueling? where does this come from xD
Yeah not displacement
Hooray one I got strait away, I'm usually slapping my head for not getting it. Thanks for the ego boost and keep the great puzzles coming.
the correct answer is 338.07 km (and that's what i got) and not 337.818 and that's because you miscalculated 100/8=12.5 and not 12.25 as you showed at 5:15
thank you
Thanks for bringing this to my notice... you are absolutely correct bro.
partial harmonic series, H16*100km = ~338.073km!
Basically: eliminate as many bikes driving as soon as you can (this eliminates the number of bikes consuming fuel)
This riddle doubles as a great explanation of asparagus staging in rocketry
Although the problem could have been worded better, the solution was very interesting! Thank you!
The phrasing of the question is wrong. As it is, I can transfer all the fuel to an external container carry it on one bike, refuel as necessary and go 1600km…
No container, they had to take a rope and go together. It would be real- good for phrasing - and close to 1600 km, now it's a question about friction force. My guess it's 1598 )
That was also presume that the additional weight of the extra fuel didn't affect the fuel economy of the motorbike to begin with.
Found someone who had a similar idea😅
KSP and asparagus staging taught me this. Gotta love interchangable knowlege
If anyone has played Kerbal Space Program and done asparagus staging, this is essentially the same principal. The exceptions being that the fuel transfer is constant as distance is covered, and that you have to drop 2 vehicles at a time rather than one to keep your mass centered.
exactly what in my mind
What a strange place to find a RuneScape legend
I would (before listening to the solution) say 338.0729km. It is given by the sum from 16 to 1 of 100/n where n is the number of bikes riding simultaneously.
The basic idea behind the formula is that the bike start all togheter and then, after 100/n km 1 of the bikes stops and share its fuel to the others bikes until 1 only bike remains.
You are more accurate!
partial harmonic series, H16*100km = ~338.073km.
Yes, I got the same result! I don't know why the answer in the video is not accurate.
What's up logical people this is Ammar😀😂
I always recite this line when I opened the VDO 😅
Now it's my habit 🤣
😄😄thanks bro :)
I'm eagerly waiting for Ur reply too good content didn't find anywhere keep working 🙏🏻❤️❤️
@@LOGICALLYYOURS I got better answer
Follow the same logic but half of the bike goes to opposite side to other half bike then we get maximum distance 543.58 km
@@aniketnikam4977 wouldnt work...asked maximum distance you can go..not the others...answer is 1600km...nowhere did it say max distance from starting point.
@@darklightwhatever6970
But you always can tow. 😁😋😋
Awesome video …. I made the similar mistake and got 300 KM …. Thank you very much for the better approach to the solution.
nearly got there. 100 / 16 .. but I thought the stop will be always 6.25.. but it should be 100 / 15 , 100 / 14 so on.. good one !
And here I thought the optimal solution yielded 1600 km traveled. The first fifteen bikes hold on to each other and the sixteenth tows them 100 km. He drops off and the second bike tows the next 100 km. Repeat for all 16 bikes and you (the sixteenth) have gone 1600 km. Well, probably closer to 1550 because of extra fuel usage for towing, but you get the point. Anyway, that is the actual optimum solution - don't run motors when you don't have to. "The best part is no part" - Elon Musk.
Logically the maximum total distance you can cover is 1600 km - the simplest way is for them all to start out together, perhaps on different roads.
Or if on 1 bike, the bike circles back to the starting point when empty to refuel.
Of course, you can go thru your calcs if you want to find the location furthest from the starting point a rider can get to. But that was not the problem statement.
@@TomTravelling just strap all the other 15 bikes onto one, and switch to another bike every 100km
@@richardklepper3299 but then one bike has to carry all the other 15 bikes so it will take lot of power on them too, but not considering that then its correct
@@gorg212 well, varying weight of the riders, wind drag, road conditions etc were all ignored as well. but it's a great thought challenge.
@@TomTravelling the problem statement was not well stated tbh...i didn't understand who the "you" was in the set-up
The explanation is really good. Keep up the quality content
There is a big loophole in the framing of the question which gives me the right to misinterpret it.. there is nowhere u mentioned that the bikes have to start at the same time neither did u say that the max distance covered is unidirectional..i could use each bike to town and back then take another bike to town and back and so on...I will have covered a distance of 1600km..
One more thing is that you are not forbidden to push à bike that has no fuel and there isnt à limited time period soo i guess you can go on for quite à while even though it might not be easy to push a motorbike like that
Every mile a motorcycle needs to drive, is fuel used out of the 1600 total fuel(km). So we want to drive bikes as little as possible. This is done by dropping out a bike as soon as its remaining fuel is just enough to top everyone else off.
At the start, that's after 100/16=6.25km. The remaining 15/16th of his fuel is divided among the other 15 bikes, which ride on. After 100/15 = 6.666 km the second bike divides its remaining 14/15th of fuel among the oter 14, and so forth.
This gets 100/16+100/15+ ... +100/2+100/1= just over 338 km.
Very nice
I am amazed by your solution but want to know that do you solve them by yourself
And where do you take such riddles from? Please answer me
Nice puzzle, but what if all the 16 bikes are in line and from rider 2 to rider 16, each rider places his foot on the bike in front of him. Then the last bike which is 16th bike is turned on and toes the next bike keeping the rest 15 bikes' ignition off. After 100km, the 15th bike is turned on and so on.
This way you dont have to transfer the fuel everytime and also you can travel 16×100=1600 km 😎😎😎
That's what I thought. But bit difficult to balance the bike i feel
@@shreyasj6437 when they dont have money to buy fuel and when they are ready to transfer fuel from one bike to other with lot of calculations, I think they can take a bit of pain to travel long distance this way🤣🤣
Just kidding 😂
@@sandeepa4116 Haha Yeah
If balancing can be an issue then what about losing some fuel by vaporization and spilling while transferring to other bikes and burning more fuel by stopping/starting on small intervals.
So you may ignore balance issue (you may tow with rope also) or you must have acknowledged above factors for given solution.
So, if you are ignoring other factors, you can tow other bikes with one bike like a train.
Towing like this will definitely not cover total distance of 1600kms but again we're ignoring other factors here also like burning more fuel by towing other bikes on neutral, balancing etc. So the answer will be 1600kms. 😁😋😋
The riddle does not preclude leaving the bike behind and walking, which means one could cover significantly more ground.
I was thinking of coasting downhill
Great puzzle!
But, believe me each and every Stop/transfer will come with some losses like vaporization, spillage, stoping/starting =% fuel usage which is generally more than rated!
Firstly i didn't get the solution, because i thought one bike on single run can go upto max 100km😉😉😉! And that my first answer.
Btw, this was good one!👍🏽
😀 thanks buddy
we always do the problems ideally even in mechanics,electrical,chemical,etc.
If we can ignore other factors like losing some fuel by vaporization and spilling while transferring to other bikes and burning more fuel by stopping/starting on small intervals.
Then you simply can tow other bikes with one bike and cover total distance of 1600kms (ignoring other factors like balancing, burning more fuel by towing other bikes on neutral, etc). 😁😋😋
Btw nice puzzle and video 👍🏻👍🏻
Hehe. I also thought the same.
Actually it can be 1600 km as you have asked maximum distance.. if it is maximum displacement, then it is 337 as you mentioned.😉
As many people in the comment section are finding out loopholes and giving different solutions, I tried myself too😉
Excellent solution without doubt, but often most of your riddles seems reverse solved. The analogy of bike with fuel is ridiculous, because, if I were to beat someones record by a mile I would rather push the bike for the extra mile. Without time constraint, this solution may not make any sense. Further, consider the spillage every time you have to refuel. Is the road flat?. Then there is "maximum distance that YOU can go", is there a space for ME to sit behind the rider. If the bike has reasonable torque then daisy chain them would be the best solution.
MINDBLOWN!
EXCEPTIONAL!
PROBLEM SOLVING @ THE PRIME TIME HERE IN THIS CHANEL
KEEP GOIN!!>>>>
Always fun to crack down your puzzles brother ! Although I manage a correct approach, but incorrect answer 😁
The most awaited video , thanks sir for uploading this video and I have already watch your all videos please upload more videos as early as possible.
🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏
Yes buddy.. I'll make the videos frequently
Solved this absolutely stunning but easy problem
Wrong, 15 riders will empty their bikes and donate it to the last one so the rider will have enough fuel to drive 1 600 km. Average motorcycle fuel consumption is 4.4 l / 100 k, which is 66 liters from 15 drivers. That is a large bag or suitcase which is possible to have on bike.
As a mathematical problem, this solution does work. In practicality, time is another resource that you would need to consider. Imagine a similar scenario but with boats travelling upstream.
Ans: 338.0728993
If R is the range, and x is the number of bikes, then the answer is R/x + R/x-1 + R/x-2.. + R/ 1
Glad to get this one right, totally missed the other similar bike problem - if 3 ppl, 2 on bike and 1 walking - what is the most optimized solution in which they can travel to a destination. I couldn't even think beyond - 2 people on bike and 1 walking all the distance, no exchange 😂..
My initial approach was one guy towing the rest 15 guys until his tank empties and one among the rwst 15 takes his turn totalling to 1600kms
🤪
It would take more fuel to carry 16 bikes a certain distance than just one. Towing is not an energy-free process.
@@oenrn If you assume the fuel required is proportional to the weight, you would still get the same result: (1/16 + 1/15 + ... + 1)*100. You also improve on the time complexity (no fuel transfer) and context switching overhead (stopping and starting will reduce fuel efficiency) with zero cost for distance.
Intuitively, it makes sense that the distance comes out the same, because when rider n transfers 1/(16-n) fuel, it's as if rider n is reimbursing the fuel per rider for the distance just covered.
Legends know that this is advanced version of camel and 3000 apples 👍
Because I have done that before, I was able to solve it easily. 😎
Or... a trailer can be made from parts of some of the other bikes to haul all the tanks full of gas and be dragged by , and to feed 1 bike , trailer dropped when you are down to 1 tank of full... distance 1600km - (the drag effect of the trailer on full consumption)
Bro I have Desi approach with which
We can go upto 500 km theoretically and approximately 400 km practically.
We have 16 bikes first of all put 8 bikes another 8 bikes they can go upto 100 km after that only 8 bikes have fuel now put 4 bikes on another 4 now we can travell another 100 km
Now we have only 4 fueled bikes
So put 2 bikes on another 2 so we will be able to travel another 100 km
Now we have 2 fueled bikes put 1 one on another we will travel further 100km now we have only bike which travell upto 100 km
Total distance traveled=500km
But this solution has one problem that is milage of bikes will be decreased due to increase in weight
But I don't think that milage will be half .
1600 KM. The question was distance traveled, not how far. But, if you use Euler's number, logarithms, divide by infinity, add 3 in the 27th step of your equation. 10KM. Unless you want 11.
I calculated 500km by just towing the every other bike for 100km by the rider. So on the first 100km 8 bikes fuel will be empty and on the second 100km 4 bikes fuel will be empty and on the third 100km 2 bikes fuel will be empty and on the 4th 100km 1 bike fuel will be empty and the remaining bike will cover another 100 km which adds up to 500 km. This is much more optimal as long as there was no clause that the ignition of all bikes has to be turned on at start
Definitely jumped to the unoptimized solution and was too lazy to figure out the optimized solution.
U never fail to amaze us with ur puzzles.
If you split the bikes into two teams traveling in opposite directions, they can each travel a total of 271¹¹⁄₁₄km and end up a total distance of 543⁴⁄₇km away from each other.
That's fantastic thinking. That should be the answer.
Man. U are genius.... Are u from iit or any prestigious college?
Thanks Aritra for the appreciation. Glad to see your comment.
@@LOGICALLYYOURS my pleasure
Can we use harmonic progression to solve it mathematically.
I found that it was the harmonic series from 1-16 and looked up the value for this partial sum: ~3.38073. But I see that others have pointed out the error in the vid giving a slightly different answer.
15guys hold the front motorbike , (15 motorbikes at km 100, with 15 full tanks) do it again , and again, and you have 1.600km done
Considering that when the fuel is gone, the motorbike will ride more 1 km at least, we will have 1616km
You cannot exchange the fuel without tools. Tools are not mentioned... but that each bike has a rider?! Also "maximum distance" could also be just 1600km. Two flaws that breaks the riddle upfront.
I think this is engineering initiative in spacecrafts. Carrying more fuel would increase its weight and therefore not always lengthens the travel distance. It's like a troop of bikes dropping down empty ones to continue journey.
Thanks for the fun problem.
Slight note: your calculation at @5:18 of 100/8 = 12.25 should be 12.50, leaving an error in the total. The summation of 100/n for n=1 through n=16 is 338.073 km.
travel until the remaining fuel in one motorcycle can fill up the other motorcycles to 100%, discard empty motorcycle, rinse and repeat = (100km/16)+(100km/15)+(100km/14)+....+(100km/2)+(100km/1)= 338km
partial harmonic series, H16*100km = ~338.073km!
The goal is to discard as many bikes as soon as possible, so that you don't waste fuel on concurrent bikes when you can avoid it.
So at 6.25 (=100/16) km all bikes have burned 1/16 tank, so they have 15/16 fuel tank. You can use up one bike to fill up the others.
So at 6.25 you have 15 bikes full.
Similarly at another 100/15 = 6.66 km you will have 14 bikes full.
Etc etc
So the total distance is 100/16 + 100/15 + 100/14 + 100/13 ....... = 338 km. This is easy to calculcate with a spreadsheet like Excel.
The optimal are 16 X 100 km. You go get a screw driver, unscrew the other gaz tank, find a chariot, put the gaz tanks on it, you attach the chariot on the "first" bike, and go 1600km!
Another thing to take in account is the speed at which you "travel", more fast you go, less distance you travel!
So, saying a tank has a range of "100km" is wrong/false/imcomplete! (or at least, you need to specified a speed, which will be mandatory! 100km range.)
So if the speed is, i don't know, 100km/h (in the video is 100km/h?) (which is not the "best" speed
@@literallylegendary6594 And it is why (i will quote myself | maybe you need to learn to read) i said :
«You go get a screw driver»
and not
You use the screw driver given! (or providen)
The Strategy mentions "A milestone is reached AS SOON AS the doner bike has enough fuel which can be transferred to the other bike to fully load its tank". That could happen after 1 inch of travel, 2 feet of travel, 8 yards, 3 kilometers, 8 miles, 17 or 44 miles. Needed is a clause such as "while fully emptying its own tank". The formula clears this up some calculating this as 50. Working with 0s and 1s for many years I'm very sticky about good definitions of problems since an unclear one can cause lots of issues and rewrites.
even though i dont work with 0 and 1, i also said that you could refill ever km.
You could do the feeding continuously and the answer would be the same. Imagine the bikes somehow connected with fuel hoses. One bike feeds all the others to keep them topped up, as well as supplying its own engine, then drops out when it gets empty. With 2 bikes connected this way, one bike basically supplies both engines until it goes empty at 50km then drops out while the remaining bike has been getting topped up so still has a full tank. It’s functionally the same as his solution but with continuous transferring.
I too noticed that. I like this definition for "milestone": for N bikes riding together, a milestone is reached when the N-1 recipient bikes have enough empty space in their tanks to hold the fuel remaining in the 1 donor bike. This drives home the essential nature of a milestone: it is a point at which we can shed a bike without shedding any of the fuel remaining in the bike. Shedding a bike whenever possible minimizes the cohort's total fuel consumption per kilometer.
Always love your content❤️
Couldn’t we derive a series formula for the general case?
It's a nice problem, but you have made a rounding error by truncating the decimals. You quoted your answer to 3 decimal places but the correct answer to 3 decimal places is 338,073km, which is 0.250km further than your answer...
partial harmonic series, H16*100km = ~338.073km.
I may be thinking about this incorrectly but I'm coming up with a different answer. Here is my logic... even though there are 16 bikes at the first refuel point there will be only 15. This means the initial distance traveled to fuel up 15 bikes is 6.666 km. You would then follow the logic for 14, 13, 12, etc. to arrive at a maximum distance of 331.823 km. With exception of Milestone 9 I agree with your table. When I calculated Milestone 9 it came up to 12.5 km vs the 12.25 km shown. Great Problem! Please let me know what you think about my approach.
All 16 bikes will be 15/16 full of fuel at the first stop, including the donor bike. The donor bike has to fill up each of the other 15 bikes with 1/16 of a tank of fuel in order to top off the tanks. Since it has 15/16 of a tank the math works out perfectly. 15 bikes each need 1/16 of a tank filled and the donor has 15/16 in its own tank. Therefore the correct answer for the first stop is 100/16 which equals 6.25km. Do the math for 4 bikes and it is easier to conceptualize.
i wish the rules had been covered a little better. while you were busy siphoning gas on the side of the road 120 times, i was removing 15 fuel tanks and bringing them 1600km with me on my motorbike. or traveled to my friends house 50km away and back 16 times by riding a different bike each day. if this seems unrealistic, i think leaving 15 people stranded is unrealistic.
The theorical most optimal distance is 338,07. Hope now my message will not be removed... sum (100/x), x from 16 to 1.
You might have optimised the maximum possible distance that one of the riders can cover theoretically, but practically, riding for 50 kms before taking a break to cannibalize petrol of one of the fellow riders is not only simpler, but a consistently predictable riding break after every 50 kms helps avoid unnecessary confusion and chaos. As an experienced group rider, I can attest to the fact that as a group of 16 riders with a target distance of 300-350 kms for the final rider, 15 riding breaks is definitely not optimal compared to 4. I can easily coordinate and organise a group of 16 riders by giving them a simple directive: ride in groups of two, and after 50 kms, those of you who are riding ahead, take a 15 minutes break to prepare the next phase of the ride, during which time refill your tank from your ride partner who is staying behind, and pair up with your assigned ride partner for the next 50 kms. Can you imagine the logistic nightmare of coordinating a group of riders who will become increasingly tired and have to stop at non-uniform interval of distances, most of which are not rounded figures, but have up to 3 decimal places, which does not show up on odometer/ trip meter information display panel of any bike?! And I have not yet broached the topic of reduced fuel efficiency when you cover 338 kms with 15 breaks when compared to covering 300 kms with only 4 riding breaks. And don't even get me started on how you plan to distribute fuel in precisely equal amounts to 15 bikes in the first instance, a calculation which is not going to get easier with subsequent riding breaks, especially with some difficult prime numbers waiting in line to test your calculation skills. So you tell me: which alternative is more optimised?!😝
When I solved this I got 500 km....16 bikes will be grouped into 8 pairs.....In each pair one bike will be running and other will be switched off, basically one bike tolls the other, by placing the leg on the running bike....after 100 km, 8 bikes will be grouped into 4 pairs....after 200 km 4 bikes will be grouped into 2 pairs and after 300 km we have 2 bikes, one tolls the other....after 400 km the last bike will go another 100km so we will get as 500 km in total
Maximum distance is1600 km. Take the tanks off 15 bikes and strap them to the back of one bike. Swap empty tank with a full one every 100 km. From my time spent living in many third world countries, that is exactly what the more enterprising members of society would do.
Is there any formula for calculating those every milestone kms in single time
so the optimized result is 13% better than a no think first glance solution? Kind of underwhelming when my initial answer was 1,600km. Why are all 16 bikes on and running? You've got 15 extra divers. Siphon the gas out and carry it on one bike (since transfers are a possibility). Or if you're not going to allow storage, turn 15 bikes off and have their riders push them 100km at a time to transfer to the first bike.
1/1 + 1/2 + 1/3 + ... + 1/16 = multiple of 100 km distance
What if we take one bike at a time... Move in a circular motion and return at the starting point (circumference=100km)... Then we can do this 16 times... Then the maximum distance travelled would be 1600 km
Because we are asked for distance
A problem well defined is half solved - Charles Kettering. A clear definition would have cleared up the confusion of the maximum distance travelled versus furthest point from the start.
as measured on a globe along the circumference whose diameter is infinity and is locked in position in space ...
Because on Earth, the distance becomes shorter once you have traveled half way around where you reach a maximum. Your travel distance is less efficient the closer you get to that maximum if you do not define a flat plane. You have to time it right so that you know where the globe is relative to it's orbit and the orbit the thing you are orbiting and ... so forth. The furthest point in a fixed flat reference plane.
I think the solution is 338,072 km but anyways great problem.
partial harmonic series, H16*100km = ~338.073km!
My answer is 1,600km. One motor bike should pull all 15 bikes from behind using a rope or what. When the first bike emptied is fuel, the second bike should do the same to pull remaining 14 bikes. Then the third one pulls other 13 bikes, and so on... Until only one left and finish the ride.
i solved for 2 and then 3 and then got the the approach for 16 but not the ans as i am bit lazy🤫😂
Bhaiya, how we get to know this is the best approach or optimized solution?
Raghaw... you just have to try several combinations of milestones in case of 3 bikes... then you'll realize that the best milestone is a point where a bike can donate all its remaining fuel to the other remaining bikes to fully load their tanks. Pls give it a try.
@@LOGICALLYYOURS Thanks Bhaiya! I got the answer.
In suboptimal solution given by ammar you would notice that we are carrying all 16 bikes till 50 km whereas we were having opportunity to leave 1 bike and save fuel.
I figured it out but I thought that it is making a pattern so it can be added by some other way of progression concept but I had to add them all with calculator.
If these values can be added by some progression method then please let me know sir.
I appreciate your work
Thanks
Love this channel
Hold all hands as a chain. Use the bike one by one. Hurray.. You can go max 1600kms
Sir please explain the concepts about lateral thing, out side the box, optimization. And also explain
When we have to use those concepts
Each bike goes out 50km and then back to start, so each bike does 100km and the total distance is 1600km
1 problem here - how do you transfer fuel without tools to remove the fuel tank or a pump? Real world - where every riddle fails.
Hold each other hand making chain
Start one go 100 km then start second
😎
....
I believe the correct answer is 1600 km. I can ride each bike for 100 km, returning to the beginning. So I would travel A TOTAL DISTANCE OF 1600 KM.
So... how do you go about "proving" that your solution is optimal? While it sounds good, is it?
Quite,
as soon as you can get a guy to leave you should do so becoz he is also burning the fuel which is a waste
The video goes through the steps of proving it without explicitly calling it a proof.
axiom 1: you can travel farther with more fuel
axiom 2: for any amount of fuel, you can travel farther by burning at a slower rate
Axiom 1 implies you should never throw fuel away. Axiom 2 implies you should decrease your burn rate whenever possible without violating axiom 1.
So, start out with a full tank (axiom 1-as much fuel as you can carry) and only a single bike (axiom 2-lowest burn rate). A bike can go 100 km. To go any farther we need to carry more fuel (axiom 1), meaning we need more than one bike. But we still want to minimize fuel consumption (axiom 2), so our second most efficient option is traveling with 2 bikes. We've got two bikes with 2 tanks worth of fuel. At what point can we switch to one bike with a full tank? When they've gone 50km (1/2 their full range) and have a total of 1/2 tank + 1/2 tank = 1 tank fuel remaining. But we want to go even farther, meaning we need more fuel, meaning we need more bikes, but only one additional, and how far can that number go.... it's always (full range of 1 bike) / (number of bikes) because _that's_ precisely when you can lower your fuel consumption rate while keeping all your remaining fuel.
Distance for 16 bikes = 100km/1 + 100km/2 + 100km/3 + ... + 100km/16. As you can see, diminishing returns set in very quickly, because for each new tank of fuel we want, we can only get (range/tanks) farther.
Here's a fun reversal that might be more intuitive. Think of the tanks as filling rather than emptying. You can start out with one glass, which fills at a certain rate. Every time your glass(es) fill, you get another one, and they all fill at the same rate. Instead of emptying one tank into several partially full ones, you want to pour a portion of each full glass into a single newly added glass. Think for a bit about how to maximize the amount of tasty beverage you can get without spilling any.
@@noodle_fc As one of my college mathematics professors once told the class, "A proof is what you and I agree is a proof." I applaud your effort.
Strictly speaking, axiom #2 is not correct. There is an energy drain overhead; even at idle--with the bikes going nowhere--fuel is being burned. Optimum mileage (kilometerage?) for motorcycles is typically in the 40 - 60 mph area (I Googled it), which implies fuel flow well above that at idle.
Unfortunately, invoking the "real world" when solving a problem such as this can lead to serious levels of ever more trivial problem specifications: Is total travel time important (is the travel "time sensitive")? Do the riders rev their engines at start up? Do the riders avoid braking, turn off their engines, take the bike out of gear (avoid engine braking), and coast to a stop? Does the road topography match the conditions that applied when the 100 km capacity was determined? How heavy is each rider? Are riders maintaining an aerodynamic profile? Which way and how fast is the wind blowing? Is tire pressure... Ad nauseum.
I do like the reversal. Inverting problems often exposes solutions--and problems--that might not be evident in the initial issue statement (caution for personal safety is advised when applying the method to religion, sports and social issues).
@@billharm6006 Regarding axiom 2, in this case we can substitute "number of motorbikes" for "burn rate." Surely you would agree that no matter the conditions, running two identical motorbikes under those same conditions uses twice as much fuel! But you are correct, if I meant number of bikes I should have said that. x_X
U r besttt❣️❣️
Can this solution be possibly used by NASA?
Well if we can just transfer fuel without spilling a drop and all of it is perfect to the nanoliter etc... why can't we just ignore the laws of physics and tie them all together 1st bike pulls them all, after 100 km 1st bike is out next 1 starts pulling... bam 1600 km
Okk but I solve it by harmonic series.. that was easy to find solution and can be use for "n" number of bikes..
Pour n motos, il faut dépenser 1/n. Chaque moto dispose alors de (n-1)/n donc une moto peut distribuer aux autres ce qu’il manque pour qu’elles aient un réservoir plein donc 1/n à n-1 motos puisque (n-1)/n est égal à (n-1)*(1/n). Dans ces conditions, n-1 motos ont de nouveau leur réservoir plein, on retombe alors dans le cas de n-1 motos. Donc la somme totale des distances par rapport à l’unité donne somme des i/n pour i allant de 1à n soit 1+1/2+1/3….+1/n. Pour n=16 on obtient 3,38. Bien à vous
Very good. Slight error though as 8 bikes is 12.5 km not 12.25
Think of it like a rocket with multiple fuel tanks emptied at same rate, but you can pump fuel from one tank to other, so you ditch one fuel tank when others are empty enough to recieve all the fuel from this tank.
The correct solution is 1600 km. The question is "what is the maximum distance you can go?" With the 1st bike you can go 100 km - 50 km north and then 50 km south, then do the same for each successive bike. (*Note that the question does NOT ask the maximum distance FROM THE STARTING POINT.)
Not watched the video yet so…
Either a) 100 km, going out in a straight line (can’t carry the other 15 motorbikes with you) or b) zero, 100 km circuit where you travel 1600 km but end up in the same place you started.
in the first 100 KM the first bike moves and other bikes are connected to it with a robe then the second bike
so the answer is 1600 KM
According to me , if all 16 bikers hold each others hand and only one bike pulls all other 15 bikes. After 100km that bike petrol is finished so he is left behind and from 15 bikes one of them pull all the other 14 bikes and this goes about 1600km or nearly 1600km. And that's my optimization.
We can go 1600 km.. By attaching other 15 bike behind 1 bike and leave 15 bike neutral... After 1st bike fule over then start 14th bike and leave other 13 bike neutral... And so on... At last we go 1600 km 😂😂
Same thing first I think 😁😁😁😁😁😂😂😂😂
Got it correct in the second attempt after Seeing the wrong approach 😂🤣, BTW good question 👍👍
What if half the bikes go in the opposite direction?
partial harmonic series, H16*100km = ~338.073km.
after 1/15 of 100km, one motorcycle shares his remaining fuel with the other 15,
after 1/14 of 100km, .... 15,
etc., until the last biker drives 100km more.
Using JavaScript:
u=1; d=1;
console.log("1: "+u+"/"+d+"="+(u/d));
for(i=2;i
*One of the best channel*
If we consider the concept of one bike towing another, I think it can be further optimised.
exactly, one bike towing all the other, so 1600 km is an answer too
Superb puzzle but shouldnt the ans be 338.07?if we add all the fractions
partial harmonic series, H16*100km = ~338.073km!
Nice logic
Well you could unbolt the gas tanks from all but 1 bikes and pinch off the fuel hose with binder clips. Put them in a large backpack, and pour the gas into your tank as you go. You never said backpacks, binder clips, and unbolting the gas tank are against the rules.
Easy peasy 😄
You could also just get off the bike and walk, making the total possible distance either incalculable or 'infinite'.