Jim, Jeanne, Louis and Anne want to cross a bridge at night with only one torch. Only two people can cross at a time, they must walk together at the speed of the slower person, and their individual crossing times are 1, 2, 5 and 10 minutes respectively. How can all four cross the bridge within a total of 17 minutes?

Introduction / Context:
This classic bridge and torch puzzle tests logical reasoning, optimisation, and the ability to work with time constraints. Four people with different walking speeds must cross a bridge at night using a single torch, with only two allowed on the bridge at the same time. The challenge is to find a crossing sequence that allows everyone to cross in no more than 17 minutes, given their individual times of 1, 2, 5 and 10 minutes.

Given Data / Assumptions:

• There are four people: Jim (1 minute), Jeanne (2 minutes), Louis (5 minutes) and Anne (10 minutes).
• Only two people can be on the bridge at the same time.
• They have only one torch, and it must always be carried by someone crossing.
• When two people cross together, the time taken is equal to the slower person's time.
• The goal is to get everyone across within a total of 17 minutes.

Concept / Approach:
The key to this type of puzzle is to minimise the time spent by the slow walkers on the bridge, while using the fastest people to shuttle the torch back and forth efficiently. We must design a sequence of crossings so that the two slowest individuals (Louis and Anne) cross together only once, and the fastest individuals (Jim and Jeanne) handle most of the returns with the torch.

Step-by-Step Solution:
Step 1: First, Jim (1 minute) and Jeanne (2 minutes) cross together. Time used: 2 minutes.Step 2: Jim, the fastest, returns with the torch. Time used: 2 + 1 = 3 minutes total.Step 3: Next, Louis (5 minutes) and Anne (10 minutes), the two slowest, cross together. They move at Anne's speed, so this takes 10 minutes. Time used: 3 + 10 = 13 minutes total.Step 4: Jeanne (2 minutes), who is already on the far side, now returns with the torch to bring back the torch for the final crossing. Time used: 13 + 2 = 15 minutes total.Step 5: Finally, Jim (1 minute) and Jeanne (2 minutes) cross together again, taking 2 minutes. Time used: 15 + 2 = 17 minutes in total.

Verification / Alternative check:
We can verify the timing by summing all segments: 2 (first crossing) + 1 (return) + 10 (slow pair crossing) + 2 (return) + 2 (final crossing) = 17 minutes. All four individuals have crossed to the far side and the total time does not exceed the required limit. Any alternative sequence that sends the slow walkers separately or uses them for returns will increase the total time beyond 17 minutes.

Why Other Options Are Wrong:
Option B makes Anne cross multiple times or involves inefficient pairings, leading to a total time greater than 17 minutes. Option C and option D similarly pair slow walkers in suboptimal ways or cause extra long returns, pushing the total over 17 minutes. Only option A organises the crossings in the most efficient manner.

Common Pitfalls:
Common mistakes include sending the slowest person back with the torch, splitting the two slowest people instead of having them cross together once, or not carefully adding the total travel times. Many learners also focus on minimising individual steps rather than the overall total. Thinking strategically about who should return and when is crucial to solving this puzzle correctly.

Final Answer:
The correct strategy is described in option A, which yields a total crossing time of exactly 17 minutes.