Remember
Five People on Two Bridges, where we met five people who needed to cross two sequential bridges at night?
In this puzzle, there are six people who must cross three sequential bridges at night. As in the original puzzle, there are some difficulties on the way. These are furnished hereunder as follows:
- Each of the three bridges have the same length.
- Each bridge can only support two people crossing at a time.
- Each person has a different speed in which they cross each bridge:
1 minute, 2 minutes, 5 minutes, 7 minutes, 10 minutes, and 14 minutes.
- If two persons are moving simultaneously, then they must move with the speed of the slower person.
- They have only two flashlights between them to see in the dark.
What is the shortest amount of time it will take for all the six people to cross the three bridges?
I got 54 minutes.
In this attempt, I sent the fastest pair (1,2) out first, leaving (1) the task of bringing the light back to the slowest pair, and giving (2) the task of retrieving (1). Reversing the roles of (1) and (2) took longer, adding two minutes to the total time.
T=0, (1,2) cross B1, B2, and B3
T=2, (5,7) cross B1, B2, and B3
T=6, (1) crosses back over B3 and B2
T=9, (1) crosses back over B1
T=10, (10,14) cross B1, B2, and B3
T=23, (2) crosses back over B3
T=38, (2) crosses back over B2 and B1
T=42, (1,2) cross B1 and B2
T=52, (1,2) cross B3
T=54, finished
The movements are plotted
here.
Edited on September 19, 2022, 11:38 am
An attempt...
