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Riddle of 4 persons crossing a bridge over a river at night within 17 minutes

Bridge crossing riddle: 4 persons to cross a bridge in 17 minutes

An emergency: 4 persons have to cross a bridge in 17 mins

Bridge Crossing Riddle: 4 persons to cross a bridge at night in 17 mins. Two persons can cross at a time with crossing speeds of each different. Read on...

The 4 person bridge crossing riddle

An aged man, his wife and their daughter and son have to cross to the other side of a deep river at night over a frail old bridge.

One of them takes 1 minute to cross while second one takes 2 minutes, third takes 5 minutes and the fourth takes 10 minutes. They have to think hard for a safe way to cross because,

  • Only two can cross at a time,
  • With only one torch between them, one member must return with the torch for the next crossing, and,
  • Unless all four of them safely cross over to the other side within 17 minutes, they will be in very grave danger.

Exclude their thinking time from 17 minute time limit.

Can you help them?

Sure you can, because you have 10 minutes to find a safe way to cross. Try to solve the riddle even if you exceed the 10 minute recommended time. If you do try, you will learn analytical problem solving and appreciate the explained solution all the more.

Solution to 4 person Bridge crossing in 17 minutes riddle

Best option will be to imagine yourself as one of the four. Concentration will be better.

Stage 1: The conventional approach

Initially, it seems if the fastest person (the 1 minute person) crosses and returns each time it might work. However, this exceeds the time limit by 2 minutes (work it out).

Stage 2: Focus on best strategy: Ask Crucial Question, Find Answer and Analyze: Critical barrier identification

Without trying various combinations of passengers randomly, you must focus on the best strategy for minimum time crossing AS A WHOLE.

Question is: Who would create most difficulties in minimum time crossing? The 10 minute person first and the 5 minute person next.

Analyze: What time the 10 minute person and anyone else together take? It is 10 minutes. Same way, the 5 minute person takes 5 minutes to cross if crossing is with 1 minute or 2 minute person.

So, if the 10 minute person and 5 minute person cross in separate journeys, their total time will be as long as 15 minutes only in two crossings. The other two have to cross and the torch has to be brought back. In this worst case, it won't be possible for all four to cross in 17 minutes.

This is Worst Case Scenario analysis. And you have identified the critical barrier for safe journey across.

Once you know what can't be done, you would automatically know what must be done:

  • The two slowest persons must cross together, and they can't cross in the first or the last journeys. Who will bring back the torch! After all, none of these two must make two crossings!

This is the most important clue to the safe journey.

Now you are all set to plan the safe journey.

Proper use of Question Answer Analysis technique and Worst case scenario analysis (identifying critical barrier) helped to reach this comfortable situation.

Stage 3: More detailed analysis: Make a promising safe journey plan

You know by now, the 10 minute person and the 5 minute person must cross together in an intermediate journey (not the first or the last). So the only possibility for the first crossing will be 1 minute and 2 minute person cross together, one of them stays back and the other returns with the torch.

  • First forward and return crossing: 1 minute person and 2 minute person cross together taking 2 minutes. Just assume, 1 minute person stays back and the 2 minute person returns with the torch. Total time taken 4 minutes.
  • Second forward and return crossing: As decided, the 10 minute person and the 5 minute person cross together taking 10 minutes. The 1 minute person waiting on the other side returns with the torch. Total time taken 11 minutes and cumulative time passed 15 minutes. Now you can see the solution.
  • Third and final forward journey: The 1 minute person and the 2 minute person cross together taking 2 minutes and the total time passed is just 17 minutes.

The promising safe journey plan turns out to be the actual safe journey plan.

Food for thought: What happens if the 2 minute person stayed back and 1 minute person returned with the torch in the first return crossing?

Summary of how you have solved

To solve this problem you have,

  • Done worst case scenario analysis asking crucial question, getting answer and analyzing the answer. You have also identified the critical barrier.
  • Found out the most important clue for the safe journey based on what you cannot do. With the clue, making a safe journey plan was dead easy.

All the decisions and steps explained were based on common sense reasoning and no special knowledge. I believe everyone has that elusive common sense reasoning and ability to identify what stands in the way of solution, not just gut feeling, intuition or hunch.

Once you have used question, answer analysis technique, done worst case scenario analysis and critical barrier identification, you will agree that it was all some form of common sense reasoning needing no special knowledge or ability.

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