Interview Riddle - 16 Bikes || Logic and Optimization Puzzle

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:

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[piyushborse]

Is it only me who thought attaching bikes with the ropes, a perfect indian solution

[pintokitkat]

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? '

[namdoolb]

Mathematically optimal, but possibly not practically so:

You gain just over 12% distance over the unoptimised solution, but have to stop 4× as many times, and the siphoning operation at each stop is much more complex because instead of each donor bike donating to one other bike it's donating to x other bikes.

You'll gain a little ground, but at a considerable cost in time.

Now, I realise the bike scenario is an abstract & that you are demonstrating a mathematical concept.
But this does also demonstrate that the best solution is sometimes the one that is "good enough".

[Jeffsd]

Interesting problem, clever solution. I figured out the concept, but had Excel do the math. Unfortunately, you miscalculated one number - Milestone #9 is 12.5 km, and the correct answer is 338.07 km

[deepmayekar]

My brain just assumed a circular track and calculated 1600 km distance 😅

[JoaoManuelCanelas]

start 1 bike, ride it for half tank in one direction, reverse until you're back at the starting point. Repeat process to any bike that you haven't rode yet until there's none left.
Distance travelled: 1 600 km

[stevendoyel]

Basically: eliminate as many bikes driving as soon as you can (this eliminates the number of bikes consuming fuel)

[lab]

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.

[DJSaez-llor]

Although the problem could have been worded better, the solution was very interesting! Thank you!

[IanDangerfield]

You guys! I was able to solve this with the optimal solution and code it in python before seeing his solution. It's significant to me because it's the first time I've solved something from scratch. As already mentioned the end total distance traveled is actually 338.07km. Thank you for the challenge!

[anandgurumurthy]

What if I rode 50 km and came back to same point 16 times. I would have covered a distance of 1600 kms without going anywhere though but I would have covered the distance.

[WgdVids]

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.

[HenryCabotHenhouse]

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.

[jdmbone]

Take the tanks off of the 15 other bikes and swap them out every 100km for a total of 1600km

[sorsocksfake]

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.

[Anoxonamoon]

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

[sergeyg]

For 8 bikes, the value should be 12.5, not 12.25, I believe.

[emem]

That's cool solution to optimize but only in one dimension. Just imagine time needed to transfer the fuel every few km...

[ExaltedwithFail]

KSP and asparagus staging taught me this. Gotta love interchangable knowlege

[ankanathharsha]

MINDBLOWN!
EXCEPTIONAL!
PROBLEM SOLVING @ THE PRIME TIME HERE IN THIS CHANEL
KEEP GOIN!!>>>>