Problem 280
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- Lord_Farin
- Posts: 239
- Joined: Wed Jul 01, 2009 9:43 am
- Location: Netherlands
Problem 280
Problem 280 (View Problem)
There seems to be some ambiguity. Is 'the upper row' the same as 'the top row'? ie does the ant drop the seed on the 2nd row or on the 5th row (measured from the bottom)?
I am inclined to think it's the 5th, though I would like a definite answer.
There seems to be some ambiguity. Is 'the upper row' the same as 'the top row'? ie does the ant drop the seed on the 2nd row or on the 5th row (measured from the bottom)?
I am inclined to think it's the 5th, though I would like a definite answer.
Re: Problem 280
Every seed is dropped on the fifth row (counted from the bottom).
Re: Problem 280
Hello, I have a question:
This is a valid starting position:
00000
00000
00000
00000
11111
This is a valid endgame position:
11111
00000
00000
00000
00000
Is this a valid endgame position?
00005
00000
00000
00000
00000
Also, is the answer of the form:
XX.49XXXX
Thanks.
This is a valid starting position:
00000
00000
00000
00000
11111
This is a valid endgame position:
11111
00000
00000
00000
00000
Is this a valid endgame position?
00005
00000
00000
00000
00000
Also, is the answer of the form:
XX.49XXXX
Thanks.
Re: Problem 280
It seems like you have four questionsx10 wrote:Hello, I have a question:
Yes.This is a valid starting position:
00000
00000
00000
00000
11111
Yes.This is a valid endgame position:
11111
00000
00000
00000
00000
No: The problem statement says:Is this a valid endgame position?
00005
00000
00000
00000
00000
"The ant will drop the seed on the first empty square of the upper row it eventually reaches."
That kind of question has nothing to do with understanding the problem, so it cannot be answered.Also, is the answer of the form:
XX.49XXXX
Thanks.
Re: Problem 280
my ant always needs between 380 and 480 steps but i just dont know how to enter that result.
"Give your answer rounded to 6 decimal places."
what does that mean?!?!
i think that sentence has nothing to do with understanding the problem - i just want to know how to enter my result - it's annoying me!
example of my ant walking around randomly (the last steps)
"Give your answer rounded to 6 decimal places."
what does that mean?!?!
i think that sentence has nothing to do with understanding the problem - i just want to know how to enter my result - it's annoying me!
example of my ant walking around randomly (the last steps)
Code: Select all
11130
00000
00000
00000
00100
11310
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00000
00000
00100
11130
00000
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00000
00100
11110
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Re: Problem 280
Suppose you flipped a coin 11 times and counted how many heads you got. Most of the time you would get somewhere between 4 and 7 - but the exact average number of heads you would get is exactly 5.5.
You have to specify how many steps the ant would average if you ran the simulation a very large number of times.
You have to specify how many steps the ant would average if you ran the simulation a very large number of times.
Re: Problem 280
so my solution doesn't work, as i had to run the simulation about 1000000000000000 times, right?
Re: Problem 280
10^{14} simulations would suffice, yes, but that's not feasible within the 1-minute rule (or the 1-year rule )
You need to think of an exact way to calculate the expectation. Good luck!
You need to think of an exact way to calculate the expectation. Good luck!
Re: Problem 280
Ok, so I think I've got a handle on the maths required for this, but my very very simple brute force simulation is producing some odd values.
So, starting from the middle square:
00000
00000
00X00
00000
11111
would the actual expected value of the number of turns it takes to reach the N'th item on the bottom row be more along the lines of {~27,~24,~19,~24,~27} turns? Because that seems really high to me.
The equivalent 3x3 scenario is giving me the equally odd numbers:
000
0x0
111
E = {~7,~4.5,~7}
Am I wildly off base here & should look into my brute force simulation, or are these close enough to the actual values that I can start delving into formulas & good stuff?
So, starting from the middle square:
00000
00000
00X00
00000
11111
would the actual expected value of the number of turns it takes to reach the N'th item on the bottom row be more along the lines of {~27,~24,~19,~24,~27} turns? Because that seems really high to me.
The equivalent 3x3 scenario is giving me the equally odd numbers:
000
0x0
111
E = {~7,~4.5,~7}
Am I wildly off base here & should look into my brute force simulation, or are these close enough to the actual values that I can start delving into formulas & good stuff?
ex ~100%'er... until the gf came along.
Re: Problem 280
I haven't checked the numbers exactly, but they don't look strange to me. For example, in the 3x3 case, if you are aiming for the bottom square, three quarters of the time you are moving further away from it in the first turn, so you would expect it would take several more turns before you get back there. For the two corner squares, even after you finally reach something adjacent to the corner, two thirds of the time you move away again.
I think you should be able to trust your brute force program.
I think you should be able to trust your brute force program.