Please show all of your work so that I can understand and follow along. If you s

Question

Please show all of your work so that I can understand and follow along. If you skip steps and/or I can't follow your logic, I will refund my points.

There are n cars on a circular track, and amongst them there is enough gas for 1 car to make a complete loop around the track. Show that there is 1 car that can make it completely around the track by pooling gas from every car that it passes by. Though other techniques than mathematical induction can be used to prove this, please use induction to do so. If you can't come up with an inductive proof but can provide another one, please do so for partial credit.

Explanation / Answer

step :1

suppose there is only one car in circular track. as it is given , enough gas is there for 1 car to make complete loop around track. therefore, as only one car present, it peacefully makes the loop.

step:2

suppose there are n cars and there is enough gas in all of them on a whole for 1 car to complete loop, assume it is true that car can make a complete loop by pooling gas from 'n' cars it passes by

step:3

suppose there are 'n+1' cars, it has been provided from step:2 that 1 car can complete loop by pooling gas from 'n' cars. now we have 'n+1' , which gives us an extra car . as 'n' is enought o complete loop, car will complete loop when 'n=1' is present also.

Thus, b the principle of amthematical induction, given statemetn is true for any number of cars

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