River crossing puzzles? Really?

While preparing for various interviews I came across river crossing puzzle with small variations quite often.

Examples:

  1. There are 4 men who want to cross a bridge. They all begin on the same side. You have 17 minutes to get all of them across to the other side. It is night. There is one flashlight. A maximum of two people can cross at one time. Any party, who crosses, either 1 or 2 people, must have the flashlight with them. The flashlight must be walked back and forth; it cannot be thrown, etc. Each man walks at a different speed. A pair must walk together at the rate of the slower man’s pace. Man 1: 1 minute to cross; Man 2: 2 minutes to cross; Man 3: 5 minutes to cross; Man 4: 10 minutes to cross
  2. Try to carry Wolf, Goat and Cabbage across a river in a boat. You can take on the boat with you only one of them in each trip. If you leave Wolf and Goat on the same bank, Wolf will eat Goat. If you leave Goat and Cabbage on the same bank, Goat will eat Cabbage. Although, they will never eat one another while you stay with them. Make sure they all safely reach the other river bank.
  3. Once upon a time a farmer went to market and purchased a fox, a goose, and a bag of beans. On his way home, the farmer came to the bank of a river and hired a boat. But in crossing the river by boat, the farmer could carry only himself and a single one of his purchases – the fox, the goose, or the bag of the beans.If left alone, the fox would eat the goose, and the goose would eat the beans.The farmer’s challenge was to carry himself and his purchases to the far bank of the river, leaving each purchase intact. How did he do it?
  4. In the missionaries and cannibals problem, three missionaries and three cannibals must cross a river using a boat which can carry at most two people, under the constraint that, for both banks, if there are missionaries present on the bank, they cannot be outnumbered by cannibals (if they were, the cannibals would eat the missionaries.) The boat cannot cross the river by itself with no people on board.
They might seem hard to solve, especially if it’s the first time you see them, it’s important to notice the similarities in these puzzles. Once you do, they will look surprisingly easy.
Example 1 exploits the idea that Man 3 and Man 4 should go together to save time – which is true, but only in certain circumstances. The trick in this case is to use one fast man to carry the flashlights so that you’re not forced to make costly crossing with Man 3 or Man 4.
A possible solution is:
  • Time 0:   Man 1, Man 2, Man 3, Man 4   –
  • Time 2:   Man 3, Man 4                                 –   Man 1, Man 2
  • Time 3:   Man 1, Man 3, Man 4                  –   Man 2
  • Time 13: Man 1,                                               –   Man 2, Man 3, Man 4
  • Time 15: Man 1, Man 2                                  –   Man 3, Man 4
  • Time 17:                                                              – Man 1, Man 2, Man 3, Man 4

So the trick is to have an low cost man (Man 1 or Man 2) on the other side of the river so that once Man 3 and Man 4 are there we avoid moving them across the river.

Example 2 replaces time constraints with dependency constraints. By trying some possible combinations you notice that you run into constraint problems as the Goat can both be eaten by the Wolf and eat the Cabbage.
A possible solution is:
  • Man, Wolf, Goat, Cabbage   –
  • Wolf, Cabbage                          –   Man, Goat
  • Man, Wolf,Cabbage                –   Goat
  • Cabbage                                      –   Man, Wolf, Goat
  • Man, Goat, Cabbage               –   Wolf
  • Goat                                              –   Man, Wolf, Cabbage
  • Man, Goat                                   –   Wolf, Cabbage
  •                                                         –  Man, Wolf, Goat, Cabbage
As you’ve seen, the trick is to leave the Wolf and the Cabbage together as they are not conflicting and move the rest around according to the constraints.
Example 3 and Example 4 can be solved in a similar fashion.
However, the purpose of this post is not to solve these puzzles as there are plenty of solutions out there on the internet.
I am somewhat surprised that this kind of questions would even be considered in an interview. They are not testing any particular area of knowledge, probably even a child with a little imagination, or why not, luck, could solve them.
 The question remains, why would someone ask an potential employee such questions?  They are indeed testing one’s creativity and imagination and his ability to think outside the box. But during an interview, when at stake is your future job and when any word or solution could endanger it, are you really able to use your imagination? Aren’t people prepared with dozens of similar questions beforehand for being able to provide an quick and correct answer?
The employer wants creative people, the best and the brightest, but during an interview the testing strategy should be different. Being aware of the stress level an potential employee can reach during an interview session is essential for accurately assessing one’s capabilities.
In an interesting video on ted.com, Dan Pink talks about the connection between money and creativity. In a way, betting your future in the company interviewing you, inhibits in my opinion  that creativity. Current interview techniques should only focus on testing technical knowledge.
For testing one’s creativity and imagination other techniques could  and should be used.
Here is the video I was talking about: Dan Pink on the surprising science of motivation  http://www.ted.com/talks/lang/eng/dan_pink_on_motivation.html

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