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# Bombing riddle

Sun 11 Jun, 2017 03:09 am
I have the following riddle and would really appreciate it if someone could help me out: some bombers needs to bomb a destination that's X KM away from them. Each of the bombers has a gas tank for 1000 KM. It's enough for one bomber to reach the destination to complete the mission, but ALL bombers must return to the starting point. Bombers spend NO FUEL on landing/departing, or on staying still in the air - meaning gas is only spent on flying a distance. Bombers can fuel each other when standing still in the same location. Now there are 3 questions, any help here would really help me.

What's the farthest destination that 3, 4, and 5 bombers can reach? Prove.
How many bombers does it take to bomb a destination that's 5000 KM away?
Does for every value of X exist a number of bombers that can complete the task? If so, what's that number as a function of X? If not, prove why not.
Thanks a lot!
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centrox

1
Sun 11 Jun, 2017 03:10 am
I bet the RAF didn't plan Operation Black Buck this way in 1982.
Kolyo

1
Sun 11 Jun, 2017 11:04 am
@felisimo,
felisimo wrote:

I have the following riddle and would really appreciate it if someone could help me out: some bombers needs to bomb a destination that's X KM away from them. Each of the bombers has a gas tank for 1000 KM.... ALL bombers must return to the starting point.

First, please clarify, does this mean a single bomber, on it's own fuel, could make a round trip to and from a destination 500 km away? Or does it mean a single bomber could make a round trip to and from a destination 1000 km away?
Kolyo

1
Sun 11 Jun, 2017 11:06 am
@felisimo,
Whatever your answer to my last question, I recommend that you first consider the case of two bombers, then three, and then try to generalize the pattern.
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centrox

2
Sun 11 Jun, 2017 11:19 am
@felisimo,
This looks like a variation of the Jeep Problem:

https://en.wikipedia.org/wiki/Jeep_problem
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felisimo

1
Sun 11 Jun, 2017 02:40 pm
@Kolyo,
It means the first thing you wrote - the bomber can fly 1000 KM all-together...so it can fly by itself and return from a destination of 500 KM.
I have tried with small numbers but I don't know how to prove that I am getting to the farthest point possible.
Kolyo

1
Sun 11 Jun, 2017 03:18 pm
@felisimo,
Maybe you can find a proof of the answer to the jeep problem.

Centrox is right: this problem is equivalent to that one.
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Kolyo

2
Sun 11 Jun, 2017 03:49 pm
As for a proof, I would derive a formula for the maximum possible distance they can travel in terms of how many airplanes there are, instead of the inverse of that which they seem to want. Prove the formula by induction, if you're familiar with that.
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WhoAmI1004

1
Wed 14 Jun, 2017 12:32 am
@centrox,
3 bombers-750Km
4 bombers-800Km
5 bombers-833.333....Km
and so on...

N bmbers---> 1000n/(n+1) Km

Doesn't matter how many bomber used, maximum distance is 999.9999... Km.
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