Paper/Pencil Problems
Re: Paper/Pencil Problems
Problem 218 (View Problem) is doable by pen and paper as also noted by several in the problem thread.
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Re: Paper/Pencil Problems
I solved problem 27 in my head. Actually I did not prove that the polynomial I found is optimal but I entered my solution and it was accepted. I published the solution way int the thread of problem 27.
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Re: Paper/Pencil Problems
If you consider using Wolfram Alpha as part of Paper/Pencil, then I would include Problem 444 (View Problem).
It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment.
Re: Paper/Pencil Problems
Problem 286 (View Problem) - Scoring probabilities.
If you don't mind doing lots of lots of non-integer multiplications.
A calculator is actually not accurate enough for this problem, as the answer demands at least 12 significant digits.
So if you don't use a computer, you will have to do it by hand
If you don't mind doing lots of lots of non-integer multiplications.
A calculator is actually not accurate enough for this problem, as the answer demands at least 12 significant digits.
So if you don't use a computer, you will have to do it by hand
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Re: Paper/Pencil Problems
Problem 52 can be solved without a computer, or even paper and pencil.
I remember just writing in the answer after one of my lectures at Uni.
I remember just writing in the answer after one of my lectures at Uni.
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Re: Paper/Pencil Problems
Problem 106 is possible with pencil and paper. It can be interpreted as a combinatorial problem.
Re: Paper/Pencil Problems
Again, If you consider using Wolfram Alpha as part of Paper/Pencil, then I would include Problem 235 (View Problem).
Re: Paper/Pencil Problems
Problem 209 (View Problem) I'd taken a long hiatus from PE. Good to be back.
Fun problem! The paper/pencil solution posted on the solution thread is brilliant. I did however find the group presentationstijn263 wrote: ↑Fri Feb 04, 2011 10:24 am Problem 208 (View Problem) too (although I needed a little help from excel )
Re: Paper/Pencil Problems
The general version of Problem 599 (i. e. how many different cubes there are for n colors) can be simplified to a pretty short expression.
Problem 84 sux!!!
Re: Paper/Pencil Problems
I did Problem 312 with a combination of paper/pencil to store some numbers and calculator for some big calculations that can be done by WolframAlpha. So you can simplify it to a single expression, although that would be pretty long and ugly.
Problem 84 sux!!!