The bridge crossing

Visual trapsLevel 1 · Starter · ●○○○○

Four people need to cross a bridge at night. They only have one flashlight and the bridge can only hold two people at a time.

Ana takes 1 minute to cross, Bea takes 2 minutes, Carlos takes 5 minutes and David takes 10 minutes. When two people cross together, they go at the speed of the slower person.

What is the minimum time everyone can cross the bridge?

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Hints

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Critical rules: You need the flashlight (there is only one).
That is why it is advisable that 10 and 5 cross only once (together), and that 1 and 2 take turns bringing the flashlight.
Optimal sequence (17 minutes): Ana + Bea cross: 2 min.

Solution

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Answer: 17 minutes
Problem details:

Person	Crossing time
Anna	1 min
Bea	2 min
Carlos	5 min
David	10 min

Critical rules:

Maximum 2 people at a time
They need the flashlight (there is only one)
Speed of torque = speed of SLOWEST

Optimal sequence (17 minutes):

Step	Action	Weather	Accumulated
1	Ana + Bea cross	2 min	2 min
2	Ana returns	1 min	3 min
3	Carlos + David cross	10 min	13 min
4	Bea returns	2 min	15 min
5	Ana + Bea cross	2 min	17 min

Key idea:

The two slowest (Carlos and David) MUST cross together
to minimize "wasted" time

Why it is optimal (intuitive):

The bottleneck is the 10 and 5 minute crossings.
What needs to be minimized is the number of times you “force” a slow person to cross.
That is why it is advisable that 10 and 5 cross only once (together), and that 1 and 2 take turns bringing the flashlight.

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