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Programming Puzzle 25 - The Great Escape

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  • Programming Puzzle 25 - The Great Escape

    ' There are 100 prisoners in 100 separate locked cells.
    ' There are 100 guards who visit the cells during the night.
    ' The first guard visits all 100 cells.
    ' The second guard visits every other cell.
    ' The third guard visits every third cell.
    ' ... and so on
    ' Until, finally, the 100th guard visits the 100th cell.
    '
    ' Now here's the catch. When a guard visits a cell he or she
    ' locks the cell door if it's open, and unlocks the cell door
    ' if it's locked.
    '
    ' After the last guard has done his duty, prisoners in cells
    ' with open (unlocked) doors can escape. In the morning,
    ' how many prisoners have escaped? For extra credit can
    ' you tell us which cells were left open?
    '
    ' Write your answer to the trace window.
    '
    ' Have fun!
    '
    ' Credit plus.maths.org

  • #2
    Re: Programming Puzzle 25 - The Great Escape

    What is the status of the doors prior to the first guard checking?
    Andrew

    Comment


    • #3
      Re: Programming Puzzle 25 - The Great Escape

      Andrew, have a cup of coffee, then read the first line of the puzzle carefully.

      -- tom

      Comment


      • #4
        Re: Programming Puzzle 25 - The Great Escape

        doh! I withdraw my previous question.
        Andrew

        Comment


        • #5
          Re: Programming Puzzle 25 - The Great Escape

          Chances are good my calculation is wrong but I am sure the Professor will be kind enough to correct me.
          Attached Files
          Andrew

          Comment


          • #6
            Re: Programming Puzzle 25 - The Great Escape

            Andy, Looks good to me. However, working it out on paper with only 10 and 10, I get 5 and 5. So I imagine the 50% would be the same for 100 ?
            Regards
            Keith Hubert
            Alpha Guild Member
            London.
            KHDB Management Systems
            Skype = keith.hubert


            For your day-to-day Needs, you Need an Alpha Database!

            Comment


            • #7
              Re: Programming Puzzle 25 - The Great Escape

              Second go; first had a few mistakes. Am very curious to see what others come up with for a solution.
              Attached Files
              Andrew

              Comment


              • #8
                Re: Programming Puzzle 25 - The Great Escape

                Hi Andrew,

                This looks much better. This puzzle is along the lines of Josephus Problem.
                Regards
                Keith Hubert
                Alpha Guild Member
                London.
                KHDB Management Systems
                Skype = keith.hubert


                For your day-to-day Needs, you Need an Alpha Database!

                Comment


                • #9
                  Re: Programming Puzzle 25 - The Great Escape

                  hello
                  here is my solution. but somehow i am getting 9. i do not know why.

                  Code:
                  dim n as n
                  dim cell[100] as c
                  for n = 1 to 100
                  	cell[n]="locked"
                  	'trace.writeln(cell[n]+crlf())
                  	next n
                  dim guard as n
                  dim pass as n
                  for pass = 1 to 100
                  	for guard = 1 to 100 step pass
                  	if cell[guard]="locked" then
                  	    cell[guard]="open"
                  	    else
                  	    cell[guard]="locked"
                  	end if
                  		next guard
                  next pass
                  dim open as n=0
                  dim i as n
                  trace.clear()
                  for i = 1 to 100
                  	if cell[i]="open" then
                  		trace.writeln("cell number " + i + "was left open")
                  	    open = open+1
                  	end if
                  	next
                  		trace.writeln("Total number of " + open + " prisioners will escape")
                  	'msgbox("Open Cells",str(open) + " Prisioners will escape when all is done")
                  	end
                  Last edited by GGandhi; 05-31-2012, 04:42 AM.
                  thanks for reading

                  gandhi

                  version 11 3381 - 4096
                  mysql backend
                  http://www.alphawebprogramming.blogspot.com
                  ggandhi344@gmail.com
                  Skype:ggandhi344@gmail.com
                  1 914 924 5171

                  Comment


                  • #10
                    Re: Programming Puzzle 25 - The Great Escape

                    hello
                    the cell number 1 should have been left open but in mine it was closed. so i changed to while...end while and now the result is 10, which i think is correct.

                    Code:
                    dim n as n
                    dim cell[100] as c
                    for n = 1 to 100
                    	cell[n]="locked"
                    	'trace.writeln(cell[n]+crlf())
                    	next n
                    dim guard as n
                    dim pass as n
                    pass = 1
                    while pass < 100
                    	for guard = 1 to 100 step pass
                    	if cell[guard]="open" then
                    	    cell[guard]="locked"
                    	    else
                    	    cell[guard]="open"
                    	end if
                    		next guard
                    pass = pass + 1
                    end while
                    dim open as n=0
                    dim i as n
                    trace.clear()
                    for i = 1 to 100
                    	if cell[i]="open" then
                    		trace.writeln("cell number " + i + " was left open")
                    	    open = open+1
                    	end if
                    	next
                    		trace.writeln("Total number of " + open + " prisioners will escape")
                    	'msgbox("Open Cells",str(open) + " Prisioners will escape when all is done")
                    	end
                    thanks for reading

                    gandhi

                    version 11 3381 - 4096
                    mysql backend
                    http://www.alphawebprogramming.blogspot.com
                    ggandhi344@gmail.com
                    Skype:ggandhi344@gmail.com
                    1 914 924 5171

                    Comment


                    • #11
                      Re: Programming Puzzle 25 - The Great Escape

                      Gandhi,

                      The professor applauds your effort, but has a couple of small bones to pick with you.

                      I don't fully understand his comments, but maybe they'll mean something to you.

                      Your code:
                      Code:
                      pass = 1
                      while pass < 100
                      	for guard = 1 to 100 step pass
                      	    if cell[guard]="open" then
                      	        cell[guard]="locked"
                      	    else
                      	        cell[guard]="open"
                      	    end if
                      	next guard
                              pass = pass + 1
                      end while
                      1) The professor thinks your While ... End While code block never reaches the 100th guard, since the block is exited when pass equals 100.

                      2) In the For ... Next block the professor insists that all 100 guards visit door 1, when only guard #1 should visit that cell.

                      3) The professor applauds your use of the "step" parameter in the For ... Next block. Very clever, grasshopper!

                      Comment


                      • #12
                        Re: Programming Puzzle 25 - The Great Escape

                        Manually I have
                        1=open
                        2=locked
                        3=locked
                        4=open
                        5=locked
                        6=locked
                        7=locked
                        8=locked
                        9=open
                        and 10 = locked

                        Which is the same as Andrew's solution. (His is better than mine as it goes all the way).
                        Regards
                        Keith Hubert
                        Alpha Guild Member
                        London.
                        KHDB Management Systems
                        Skype = keith.hubert


                        For your day-to-day Needs, you Need an Alpha Database!

                        Comment


                        • #13
                          Re: Programming Puzzle 25 - The Great Escape

                          hello

                          thanks
                          i looked at the result of both solutions presented and
                          the outcome from mine was wrong. while total remains correct.(different prisoners will get out)
                          will need to clean up the thinking process.

                          thanks again
                          thanks for reading

                          gandhi

                          version 11 3381 - 4096
                          mysql backend
                          http://www.alphawebprogramming.blogspot.com
                          ggandhi344@gmail.com
                          Skype:ggandhi344@gmail.com
                          1 914 924 5171

                          Comment


                          • #14
                            Re: Programming Puzzle 25 - The Great Escape

                            Keith, you're on the right path. Only 90 more guards to go!

                            Comment


                            • #15
                              Re: Programming Puzzle 25 - The Great Escape

                              All my guards came out on strike!!!
                              Regards
                              Keith Hubert
                              Alpha Guild Member
                              London.
                              KHDB Management Systems
                              Skype = keith.hubert


                              For your day-to-day Needs, you Need an Alpha Database!

                              Comment

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