Bridge and torch puzzle

Four people need to cross a bridge at night which only supports two people at the same time. Person A needs 1 minute to cross the bridge, B needs 2 minutes, C needs 5 minutes and D needs 10 minutes. When two people cross the bridge they move at the slowest person’s pace.  They have a torch which has battery left for only 17 minutes. They can’t cross the bridge without light. How can they manage to cross the bridge?

One might guess that an obvious solution would be to let the fastest person (A) shuttle each other person over the bridge and return alone with the torch. This would give the following schedule:

A, B -> 2
A <- 1
A,C -> 5
A <- 1
A,D -> 10

The total duration of this schedule would be 19 minutes, so the torch would run out of battery while person A and D are still on the bridge.

The optimal solution consists of letting the two slowest people (C and D) cross the bridge together, giving the following schedule:

A, B -> 2
B <- 2
C,D -> 10
A <- 1
A,B -> 2

Which gives a total crossing time of exactly 17 minutes.

Writing a prolog program to solve this kind of river crossing problems is a walk in the park. Check it out if you want to know an alternative solution.

Happy birthday to Benoît Mandelbrot

Today the father of fractal geometry turns 83. Benoît Mandelbrot is known for the Mandelbrot set, a set of points in the complex plane that forms a fractal. To see if a point c belongs to the Mandelbrot set start with z0 = 0 and generate the sequence z1, z2, z3,.. by iterating the function zn+1 = zn2 + c. If the value z remains close to the origin, the value c belongs to the Mandelbrot set. If it runs away to infinity, it doesn’t. Plotting the set of points in the complex plane gives you this picture.

mandelbrot.jpg

The picture is the result of running a small program I wrote on the TI-83+ calculator. You can download it from here. The program runs for several hours. The zip-file also includes two of my other TI-Basic fractal programs. A Julia fractal and the Sierpinski triangle.

Prolog solution to Einstein’s riddle

The following puzzle is said to be invented by Einstein. Supposedly, he also claimed that only 2% of the world’s population would be smart enough to solve it.

There are 5 houses in 5 different colors in a row. In each house lives a person with a different nationality. These 5 owners drink a certain drink, smoke a certain brand of cigar, and keep a certain pet. No owners have the same pet, smoke the same brand of cigar or drink the same drink.

The question is: WHO OWNS THE FISH?

HINTS:

  • the Brit lives in the red house
  • the Swede keeps dogs as pets
  • the Dane drinks tea
  • the green house is on the immediate left of the white house
  • the green house owner drinks coffee
  • the person who smokes Pall Mall rears birds
  • the owner of the yellow house smokes Dunhill
  • the man living in the house right in the center drinks milk
  • the Norwegian lives in the first house
  • the man who smokes blends lives next to the one who keeps cats
  • the man who keeps horses lives next to the one who smokes Dunhill
  • the owner who smokes Bluemaster drinks beer
  • the German smokes prince
  • the Norwegian lives next to the blue house
  • the man who smokes blends has a neighbor who drinks water

Working out the solution with nothing more that a pen and some paper is certainly doable by, I suspect hope, a larger percentage of people than the 2 % mentioned above. But as an example of how to solve these kinds of logic puzzles using Prolog, I wrote this code.

Sudoku solver

It’s pretty straightforward to make a Sudoku solver in Prolog especially when applying CLP (Constraint Logic Programming).

Here is how to use my program:

Then you can enter the known numbers one by one.

When complete, the program determines and prints the solution.

Typing

Gives

By pressing ; over and over again, you could enumerate all 6,670,903,752,021,072,936,960 possible Sudoku solution grids, but this might take a while..

It shouldn’t be too hard to extend this program to actually create new puzzles. If anyone does, let me know.

The prolog environment I used here is SWI-Prolog.