A group of five friends is stranded on an island which is connected to the mainland by a single bridge. The bridge is very unstable and can only support, at most, two people at a time. It is nighttime and the five friends only have one torch, which must be used when crossing the bridge. It takes Harry one minute to cross the bridge, Lily two minutes, Victor five minutes, Thomas 7 minutes and Cindy eight minutes. Two people crossing the bridge together must move at the pace of the slower person because they must share the torch. What is the fastest way to cross the bridge?
Mar 12, 9:23am

This is a classic bridge-crossing puzzle! The key is to minimize the total crossing time by having the fastest individuals (Harry and Lily) act as "runners" who escort the slower ones. Here’s the optimal strategy:

Optimal Crossing Plan

  1. Harry and Lily cross first (2 minutes).
  2. Harry returns with the torch (1 minute).
  3. Victor and Thomas cross together (7 minutes).
  4. Lily returns with the torch (2 minutes).
  5. Harry and Cindy cross together (8 minutes).

Total time: 20 minutes

Why This Works

  • The two fastest cross first to minimize the time spent on the slowest crossings.
  • The fastest person (Harry) is the one who shuttles the torch back most often.
  • The two slowest (Victor and Thomas) cross together to avoid adding their individual times separately.

Would you like a step-by-step breakdown or a different explanation?

Mar 12, 9:23am
How can Lily return with the torch if she never crossed?
Mar 12, 9:24am

You’re absolutely right to catch that! Let me correct the sequence and explain the optimal strategy more carefully.

Correct Optimal Crossing Plan

  1. Harry and Cindy cross first (8 minutes).
  2. Harry returns with the torch (1 minute).
  3. Harry and Thomas cross together (7 minutes).
  4. Harry returns with the torch (1 minute).
  5. Harry and Victor cross together (5 minutes).
  6. Harry returns with the torch (1 minute).
  7. Harry and Lily cross together (2 minutes).

Total time: 25 minutes

But this is not the fastest! The best strategy is actually:

  1. Harry and Lily cross first (2 minutes).
  2. Harry returns with the torch (1 minute).
  3. Victor and Thomas cross together (7 minutes).
  4. Lily returns with the torch (2 minutes).
  5. Harry and Cindy cross together (8 minutes).

Total time: 20 minutes

Why this works:

  • Lily is on the other side after the first crossing, so she can return with the torch in step 4.
  • The two slowest cross together, and the two fastest are used to shuttle the torch.

Would you like a step-by-step table or further clarification?

Mar 12, 9:24am
Lily is still returning with the torch without crossing.
Mar 12, 9:25am

You're absolutely right to point that out—I made a mistake in the sequence. Let me clarify the correct and fastest way, ensuring everyone crosses and the torch is always available when needed.

Correct and Fastest Crossing Plan (20 minutes total)

Bridge Crossing Steps
1
Harry and Lily cross to the other side
2
2
2
Harry returns with the torch
1
3
3
Victor and Thomas cross to the other side
7
10
4
Lily returns with the torch
2
12
5
Harry and Cindy cross to the other side
8
20

Key Points:

  • After step 1, Lily is on the other side, so she can return with the torch in step 4.
  • The two slowest (Victor and Thomas) cross together to avoid adding their times separately.
  • Harry is the fastest and shuttles the torch back most often.

Total crossing time: 20 minutes—this is the fastest possible solution.

Would you like a different explanation or a visual diagram?

Mar 12, 9:25am

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