Bridge Crossing Riddle: Four Persons to Cross in 17 Minutes

Submitted by Atanu Chaudhuri on Sun, 15/11/2020 - 17:52

17 minute bridge crossing riddle

How Can the Four Persons Cross a Frail Bridge in 17 mins?

Bridge Crossing Riddle: 4 persons to cross a bridge at night in 17 mins. They have one torch, walk at different speeds and maximum two can cross together.

The 17 Minute Bridge Crossing Riddle

Four persons to cross a frail bridge at night with only one torch between them. They cross the bridge at different speeds, individually taking 1 minute, 2 minutes, 5 minutes and 10 minutes.

The bridge being weak, at most two can walk on the bridge while crossing together. They must all cross over to the other side within 17 minutes. Otherwise, they will be in great danger.

How could they cross the bridge safely?

Time for you to solve is 10 minutes.

Hint: Strategic thinking, identifying and overcoming bottlenecks needed.

Solution to the 17 Minute Bridge Crossing Riddle

Step 1. Understand the Problem

Four persons must cross a bridge at night.
Individual crossing speeds: 1 minute, 2 minutes, 5 minutes, and 10 minutes.
Total time to cross must not exceed 17 minutes.
Only two people can cross together at a time.
The group has only one torch.

⇨ The torch must be brought back on the return trip for the next crossing.

Step 2. Identify the Primary Bottleneck in Safe Crossing

Question: What is the chief hurdle in safe crossing?

⇨ Each of the two slowest 5-minute and 10-minute persons would delay the crossing. For example, if the 1-minute person and the 10-minute person cross together, the trip will take 10 minutes—the time to cross by the slowest person.

⇨ In a trip together, the delay in crossing because of the slower person is the primary bottleneck.

⇨ However, focusing on minimizing delay—a negative aspect—can make planning a safe crossing challenging. Instead, converting this delay into a positive outcome simplifies the process.

Question: Can you convert this negative property of delay to an equivalent favorable outcome of a joint trip that can be easily manipulated for a safe crossing?

Step 3. Convert the negative property of delay to a favorable outcome in a joint trip

Know more about the bottleneck of delay in a joint trip:

Consider an example: When, the 1-minute person and the 10-minute person cross together, the crossing of the 1-minute person is delayed. This delay cannot be used conveniently for discovering the clue to the solution.
Reframing the problem, the delay can be seen as a positive outcome: 1 minute of time saved. (as crossing time of the faster 1-minute person is included in the crossing time of the slower 10-minute person).
As you would know the time saved in each joint trip, it would be easy to use this favorable outcome of time saved to plan the entire safe crossing.

Negative to positive transformation problem solving technique: This is how a negative property (here, the delay) of the primary component (here, a joint trip of two persons) in a problem can be transformed to an equivalent favorable—and so, a positive—property (here, the time saved in a joint trip) to use conveniently for the ultimate solution.

In a joint trip of the 1-minute and the 10-minute person, the 9 minute delay was specific to, and felt by, the 1-minute person. Reframing the delay to 1 minute of time saving transformed it as the time saved for the entire safe crossing. This shift in perspective changes the ownership of the property:

Delay: A personal burden felt by the faster individual. Being personal, it is unwieldy in optimizing the overall trip plan.

Time Saved: A collective benefit that contributes to the group’s success.

Identifying the primary goal as maximizing the time saved is a natural next step, as it provides a measurable and actionable metric for planning the crossing.

Step 4. Identify the Primary Objective and the Primary Strategy

The primary objective:

For safe crossing, maximum time must be saved in each trip of the entire crossing.

Question: How to meet this goal?

Form the primary strategy:

To save maximum time, the two slowest persons (5-minute and 10-minute) must cross together in a single trip.

If the two cross separately, it will take 15 minutes, leaving only 2 minutes for the rest of the trips—they can't cross separately and must stay back after crossing together.

Question: Who will then return with the torch for the next trip?

Step 5: Discover the Ultimate Clue to the Strategy for Entire Safe Crossing

After the trip of the 5-minute person and the 10-minute person crossing together and staying back:

⇨ The next strategic trip: The fastest 1-minute person waiting on the other side of the bridge to bring back the torch to the near side. This will save maximum time.

⇨ But to remain waiting for the two slowest persons cross, the 1-minute person must cross the bridge before the slowest two persons cross together.

⇨ So, the 1-minute person and the 2-minute person should cross together in the very first trip, saving maximum time. The two slowest would cross together on the second trip.

All the pieces of the puzzle now fit together.

Step 6: Converting Strategies to the Safe Crossing Plan

Trips for all four persons safely crossing over in 17 minutes:

Trips for safe bridge crossing in 17 minutes

The group of four saved themselves by an intelligent strategy for safe crossing.

Key takeaway

The two slowest persons must cross together to save time, and the faster persons should handle the torch returns.

Any other way to solve?

Can you think of another way to solve this riddle?

Sum up

The key to solving this puzzle is to maximize the time saved by having the two slowest persons (5-minute and 10-minute) cross together and using the fastest person waiting beforehand (1-minute) to return with the torch.
First breakthrough was provided by converting the negative outcome of delay in a joint trip to the favorable, positive outcome of saving time in each joint trip (use of Negative to positive transformation problem solving technique).
Strategic thinking along with raising the most important question, finding its answer and analyzing the result to raise the next question at each step (the QAA problem solving technique) played the primary roles in reaching the solution elegantly.

Real-World Applications of the Techniques

The abstract problem-solving techniques used in this riddle have broad applications in real-world scenarios. Here are two striking examples of turning a negative aspect into a powerful positive outcome:

Negative to positive transformation technique:
- Nuclear Embargo on India: When a nuclear embargo was imposed on India, it was initially seen as a setback. However, India converted this negative constraint into a powerful positive outcome by developing its own nuclear capabilities. Today, India is a nuclear-enabled nation, showcasing how adversity can drive innovation and self-reliance.
- NVidia GPU Embargo and the Rise of Deepseek: When an embargo restricted access to NVidia GPUs, it seemed like a major obstacle for AI development in China. However, this limitation led to the creation of Deepseek, a groundbreaking AI system that has revolutionized the field. Deepseek's unique architecture and capabilities have challenged conventional approaches, demonstrating how constraints can spark transformative innovation.
QAA Technique (Question-Answer-Analysis):
- Business Strategy: Asking critical questions like, "What is our biggest bottleneck?" and using the answers to guide decision-making.
- Scientific Research: Formulating hypotheses, testing them, and analyzing results to refine theories.