A number theory problem by Rachit Agarwal

Number Theory Level 5

Four people need to cross a rickety bridge at night. Unfortunately, they have only one torch and the bridge is too dangerous to cross without one. The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge. Times for each person: 1 min, 2 mins, 7 mins and 10 mins. What is the shortest time needed for all four of them to cross the bridge?

answer in minutes.


The answer is 17.

Rachit Agarwal by Rachit Agarwal , 22, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Saya Suka
Apr 27, 2021

Answer
= ceiling[1,2] + 1 + ceiling[10,7] + 2 + ceiling[1,2]
= 2 + 1 + 10 + 2 + 2
= 17 minutes


0 Helpful 0 Interesting 0 Brilliant 0 Confused
Rachit Agarwal
Mar 5, 2015

17 mins

The initial solution most people will think of is to use the fastest person as an usher to guide everyone across. How long would that take? 10 + 1 + 7 + 1 + 2 = 21 mins. Is that it? No. That would make this question too simple even as a warm up question.

Let's brainstorm a little further. To reduce the amount of time, we should find a way for 10 and 7 to go together. If they cross together, then we need one of them to come back to get the others. That would not be ideal. How do we get around that? Maybe we can have 1 waiting on the other side to bring the torch back. Ahaa, we are getting closer. The fastest way to get 1 across and be back is to use 2 to usher 1 across. So let's put all this together.

1 and 2 go cross 2 comes back 7 and 10 go across 1 comes back 1 and 2 go across (done)

Total time = 2 + 2 + 10 + 1 + 2 = 17 mins

0 Helpful 0 Interesting 0 Brilliant 0 Confused

You said it was too dangerous for one to cross. Then, how did 2 come back the whole way by himself?

Vikram Venkat - 6 years, 3 months ago

Log in to reply

i said too dangerous dear but not said that "it is not possible ever"

Rachit Agarwal - 6 years, 3 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...