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Topic: 100 box problem (Read 1289 times) |
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Giannis Zertopoulis
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There is a puzzle problem that hasn't anyone solve yet. Any help would be accepted! 
There is a 10x10 table that has to be fullfilled with numbers from 1 to 100.
You begin from the upper left box with number 1.
horizontically and verically you move every three boxes, else every 2.
For example:
1 x x x x x x x x x
x x x x x x x x x x
x x x x x x x x x 10
2 x x x x x x x x x
x x x x x x x x x x
x x x x x x x x x 9
3 x x x x x x x x x
x x x x x x x 8 x x
x x x x x x x x x x
4 x x 5 x x 6 x x 7
We have managed to reach 99. Every solution given 100 would be nice!
Also accepted code that solves the problem.
E-mail me!
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Barukh
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Re: 100 box problem
« Reply #1 on: Nov 29th, 2005, 11:18pm » |
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Giannis, when you say "else every 2", you meand "diagonally", or other routes are also possible?
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Giannis
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I meant diagonally.. no other routes available!
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Grimbal
wu::riddles Moderator
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Re: 100 box problem
« Reply #3 on: Dec 2nd, 2005, 4:35pm » |
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00 13 54 01 14 55 22 05 56 23
33 65 98 34 64 97 35 63 96 36
74 40 15 75 39 04 76 38 21 77
99 12 53 02 82 87 25 06 57 24
32 66 73 85 49 72 84 62 95 37
91 41 16 88 26 03 81 27 20 78
70 11 52 71 83 86 48 07 58 45
31 67 92 30 50 93 29 61 94 28
90 42 17 89 43 18 80 44 19 79
69 10 51 68 09 60 47 08 59 46
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JCJC454
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Re: 100 box problem
« Reply #4 on: Dec 2nd, 2005, 5:00pm » |
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Just a quick question Grimbal. Very nice answer but how did you get it? Im sure you didnt sit there going through all the different permutations. There must be some sequence or mathmatical answer to which I am interested to know.
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24 beers in a case. 24 hours in the day....coincidence?? I think not.
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Grimbal
wu::riddles Moderator
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Re: 100 box problem
« Reply #5 on: Dec 3rd, 2005, 12:14pm » |
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When I read the problem, I somehow froze, just sitting there, my eyes half-open, moving erratically, until the solution flashed in front of my eyes. I did a print screen.
Just joking...
I used a trick I found for the "knight riding around the chessboard" problem. I created closed loops to cover the whole board and connected them by switching parallel steps.
One loop was going around the board (now 00-01-22-23-24-45-...). Another loop was (04-15-16-...-21) I replaced 01-22 and 21-04 with 01-04 and 21-22. Then at 04-15 I connected another loop going (05-06-07-...-14). I also replaced 01-04 by 01-02-03-04 to fill the center. You can consider (02-03) to be a small loop.
Of course, the numbers were given after connecting all the loops.
This way of doing forces me to get back to where I started (99 is just one step away from 00), but that is usually asked as an extra difficulty.
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Giannis
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Impressed! 
Well i would really apreceate if i could have the source code please! Mail it or post it!!!
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Grimbal
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Re: 100 box problem
« Reply #7 on: Dec 4th, 2005, 1:21pm » |
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Source code? Uh... I did it on paper. 
Actually, I used excel to fill in the loops with increment formulas for the step number so that when I connect 2 loops, the steps are renumbered automatically.
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Giannis
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Hello again!
I was trying to understand how you solved the problem, so I would like you to explain a little bit more the way and also tell me where can i find the
"knight riding around the chessboard" problem"" and its solution....
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