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| Spark |
| Thursday, May 22, 2008 |
This past week has been a tough one. Every day I came to the room with an exhausted mind and an exhausted heart. In the middle of the week, I got to wonder if I am really smart enough, if my brain's quality of functioning has deteriorated with time, or if the work is really that demanding and challenging.
This colleague, gave a puzzle to solve. Now I love puzzles, especially related to Math. Let me quote it here.
There is an infinite sized paper, with squares on them. In the middle is the (0,0) and the page streches on all sides infinitely. There is an invisible frog on the paper. And you have a photon gun. You have to shoot the frog with your gun. The frog starts at a random square and jumps in a pre determined direction, a pre determined number of steps everytime you shoot. You dont know where it started, or the direction or the number of squares it jumps. You can shoot how many ever times you want at any square on the paper. You will know when you have shot the frog, with the red blooody spot on the square it was in. ;--) Now your task is to device an algorithm such that you will shoot the frog in the end.
No googling.
Here is the beauty of it all.
I was working yesterday, with a dull mindset, with my inferiority complex, when this person came and asked us if we solved it. I had not even thought about the problem, on hearing it I thought it was just impossible to solve. I mean where do you start, how do you proceed? It just added to my complex. Then I asked him if he can give us a clue. He gave one. First try to solve it in one dimension, and if you know where the frog starts. Then I had a spark, or a brainwave if I may call it. I told him what I thought as I thought, and he said I just solved half the problem!! He was impressed, which made me happy obviously, and I had to explain it to the other person till he understood it!
Then we went ahead and solved it for 2D if we know where the frog starts. Unknown starting point of the frog is just another parameter in the puzzle. I havent finished solving it yet, only because I havent spent any time on it, but in puzzles its the first idea that counts and its 50% of the solution. ;--)
Now all is well in my land. There is still hope for me, my brains may be a little rusty but a little conditioning will help bring it back to good working condition. ;--) Its amazing how such a simple thing can improve my mood so much!
These are times when I wish I had more Math in my work. I work with bits and bytes and I worked on a divider, but thats all the Math I get to do.
So do give it a shot. It will be child's play for OK and other PhDs I am pretty sure.
PS: There I wrote a post without anything about Israel, I thought I will not be able to do it. :--)
Updated: I solved it. |
posted by SK @ 9:49 PM  |
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| 17 Comments: |
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Ah, just when i thought 'Israel' was missing, I found it! The word i mean :D hehe...
Puzzle noted. Solving starts...NOW! ;)
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Puzzles make me feel like those kids in school, who when questioned by the teacher feels 'What? she knows the answer and she asks so easily. Where the hell do I go for the answer?!"
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Lol! Honestly I suck at puzzles. Hey try singing no. I am bored.
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Preeeeti, tooo muchhh! :--) Solve panniacha?
Arun,
LOL! :--) Its fun to solve.
Ok,
What is this man, you are a Math pistu, how can you say this. Give it a shot, you might enjoy arriving at the solution.
Paatta, I will try, no time for now, may be next weekend. :--)
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SK, Is the problem statement complete?? Asks K btw.
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Laksh,
It is complete. Do let me know if there are specific questions, I can answer. :--))
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*head hanging low*
i never got around to solving it... :( answer plz :(
[truth is i dint try ;)]
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Oh and i dint try cuz the statement itself was too complicated for my lil brain :D
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wow -that is interesting. Breaking head...
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SK, For one-dimension, I think you need to start shooting in some kind of progression (geometric) and go back and forth starting at (0,0). Extending this for 2-D, you will have to go in a spiral (again starting at (0,0).
Does this make sense at all or am I totally off the mark?
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Sorry to hog your comment space, a slightly refined solution (from me and my better half):
For single dimension assuming the starting point is (0.0): The frog jumps everytime you shoot. So, you start shooting at square number squares (ie) (1,0), (4,0), (9,0) and so on...
Extending this for 2-D, you shoot in a spiral in the following fashion (1,0), (0,4), (-9,0), (0, -16) - basically square #s alternating on all sides and eventually you will shoot the frog.
Still trying to solve the case where the starting point is unknown...
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Preeti, :--)) Its not too complicated , if u solve is in small pieces.
A-kay! I think you get the idea! 1D is correct. 2D, is not, u need to think of 1 step in each direction and then 2 steps in each direction and get the coordinates :--)
Do let me know how it goes with the moving starting point, its interesting :--)
And I am really glad atleast one person is trying to solve it!
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aiyo...math you mean MATH? *sneaks out*
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Maybe I shud start working on my Kumon.
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WT, Hhehehe :--))
Lollypop, :--) yes and then try this puzzle may be? :--)
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Where is the full solution? :)
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Ah, just when i thought 'Israel' was missing, I found it! The word i mean :D hehe...
Puzzle noted. Solving starts...NOW! ;)