The Famous Bridge Riddles

(A Variant of this shown below):

Four people are running away from zombies. They have seventeen minutes to cross a bridge that will take them to safety.

The bridge is able to hold a maximum of two persons at the same time, and one of them has to cross while holding a lantern because otherwise the visibility is poor.

The four people include you who can cross the bridge in one minute, a lab attendant who can cross the bridge in two minutes, a janitor who can cross in five minutes and the old professor who can cross in ten minutes.

All four people have to be safe across the bridge by the end of seventeen minutes or else a zombie will step on it and break it.

There are no tricks involved like swimming or going gangsta against the zombies like Resident Evil. Your only retribution is pure logic.

A Possible Solution:

Recap the given information:
(Each can cross the bridge in how many minutes?)

Me (1 minute)
Attendant (2 minutes)
Janitor (5 minutes)
Professor (10 minutes)

So, we do it as follows:

(i) Firstly, the Attendant (lab) & I cross the bridge with the lantern, time taken (2 minutes).

(ii) Then, I return to the starting point alone carrying the lantern (1 minute).

(iii) Next, the Janitor & Professor walk with the lantern across the bridge (10 minutes).

(iv) This time, the Attendant (lab) brings back the lantern to the starting point where I am waiting (2 minutes).

(v) Finally, the Attendant (lab) & I cross the bridge to the other side to safety (2 minutes).

Total time taken for these 5 steps above:

2 + 1 + 10 + 2 + 2 = 17 minutes (as required).

Remark

This is a visual example of a powerful tool in Inequality (Mathematics) called the “greedy algorithm” & a form of the “Rearrangement Inequality” too.