Logic Quiz

[MustafaQuraishi]

Re: Logic Quiz

@SID_NY

It should be 16 then

@psyah

I sorta agree with with SID_NY but he might not be considering the light source.

Assuming that when the people start to walk in a given direction they have to continue until they get to the other side. They can’t stop on the bridge.

Then at t=0 D and B leave together - the candle is with D.
At t=4, B should be across so A can follow on to the bridge
At t=7, C can set off since only D remain on the bridge
However by t=12, C will have only completed 5/9th of its journey and there would be no light source
So A comes to the rescue and goes back collecting the light from D when it completes its journey at t=12
So A goes to the other end with candle in hand and comes back, the double trip taking 6 mins so in the last 2 minutes only A remains on the bridge. Which makes t=18

However if the people do not have to go end to end on the bridge then the time can be reduced to 16 mins, but this requires A to stop midway and align his return with C.

@Southie

@psyah and other - shoukd we assume there is onky ONE Torch / candle?

@Southie

The answers to these questions are needed. Else the problem statement is incomplete

1. How many torches are there?
2. if onky one, does this mean that folks on the bridge - max of 2- have to be at same spot with torch. OR. Can you have the torch be present ANYWHERE in the bridge, with the two persons having the freedom to be in separate locations along the bridge.

I will assume one torch. And the max of 2 persons having freedom to be in separate locations along the bridge.

@Southie

C and D set out first. D carries the torch. As soon as C reaches after 9 minutes, A sets out. A and D reached the other end at same time at t equals 12 min. D passes the torch to A at t equals 12 and steps off the bridge. A stays on the bridge near the destination side. At t equals 12 B sets off for the other side. At t equals 16 B reaches the destination. A and B step off the bridge at exactly 16 minutes.

And the fat lady bellowed.

@psyah

I don’t think staying on the bridge is allowed. Likewise, I don’t think walking halfway is allowed either. But that is an incomplete problem statement for you…

@Southie

Yes problem statement is not clear. Since it was not specified staying on bridge not allowed tbis wouod be valid solution.

I will now solve for case where staying on bridge not allowed. Or walking halfway not allowed. In other words have to go full from one side to other.

I assume exchanging torch allowed.

@psyah

With your latest assumptions the lowest I made it was 18 mins.

@Southie

^ haven’t read above post in case that has solution.

Here is solution for assumptions in previous post.

T=0. C And D set out. D has torch
T =9 C reaches. A starts
T=12. D and A reach. A takes torch. And turns around to go to start. B sets out.
T= 16. B reaches. A is 2 min from desitniation.
T =18 A reaches.

Answer 18 sec.

I thought i had cleared these assumptions in the update but i guess they weren’t cleared.

1. There is only one light source. Only one. there is no other option or no hidden way of getting another light source
2. A person can’t cross the bridge without a light source. Most of you people tried to gave the light source to D and paired it with another person (C). But in this case, C would only be able to cross the birdge at the speed of D since D is the one who is holding the light source. C can’t walk past D because if he does, he would be leading and wouldn’t have the light source to see. Similarly, If D is in the middle of the bridge with light source, another person from another end can’t start because he wouldn’t have the light source. The people at the other side has to wait for someone to bring the light source back to them.

To simplify,

1. A pair can only cross the bridge at the speed which is slowest between them. i.e. if A and D are crossing the bridge then A’s speed is irrelevant since D is walking at slower speed.
2. A single person can’t start the walk without having the light source. Consider the bridge as river and light source as boat. The speed of the boat would be the rowing speed of the slowest person.
3. There is only one light source. If A and D is carrying it and they reached the other end, then one of them has to bring the light source to the starting end to bring other people

I hope its clear now.