Paper/Pencil Problems
Re: Paper/Pencil Problems
Well, it would be a little dishonest to say yes, since the variety of methods I've been using to answer those type of question have typically been dubious (although I made the effort to solve 138 'legitimately' with a bit of basic algebraic number theory). But I cannot see why the general strategy should fail for some equations and not others, and the forums for the problems I suggested have answers from people who actually did them properly properly rather than just found something that worked or checked *that* website which solves such things for you.
Re: Paper/Pencil Problems
PE197, first time by dBlade 10 Jun 2008 10:45 am.
Entia non sunt multiplicanda praeter necessitatem
Re: Paper/Pencil Problems
That's no pencil and paper but calculator and thumb. (pun intended).Francky wrote:PE197, first time by dBlade 10 Jun 2008 10:45 am.
Re: Paper/Pencil Problems
I would say, it's possible to write a proof with pencil/paper, and finish with calculator, as mentionned in the first post of this thread.hk wrote:That's no pencil and paper but calculator and thumb. (pun intended).Francky wrote:PE197, first time by dBlade 10 Jun 2008 10:45 am.
But it's true, it's not a single expression, we have to do more than press enter.
So, I don't know, now.
You know that I don't like (I hate) solutions where people choose bounds* or methods* for their convenience, or other kind of cheat ...
* unless it's prooved.
Here, I just would say, that's "possible". (?)
Entia non sunt multiplicanda praeter necessitatem
 juanchodepisa
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Re: Paper/Pencil Problems
I'm pretty sure someone willing to perform some tedious arithmetic operations, can solve Problem 94 (View Problem). It can definitely be solved by calculator. I would have, but couldn't be bothered (rather coded some Python )
 Rainy Monday
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Re: Paper/Pencil Problems
I'd say Problem 33 (View Problem) is a fine example too.

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Re: Paper/Pencil Problems
I'm almost certain that Problem 44 is possible with pen and paper.
I just haven't quite worked out exactly how yet
Will update when/if I get there.
I just haven't quite worked out exactly how yet
Will update when/if I get there.
 PurpleBlu3s
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Re: Paper/Pencil Problems
I nearly tried 107 by hand. If I can be bothered I may still try, because I don't think it would take that long using the algorithm I coded to solve it. It would be similar to doing 96 (Su Doku problem) by hand although far less work, but still fairly tedious.

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Re: Paper/Pencil Problems
You can also solve 205 with a pencil and paper.
 Marcus_Andrews
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Re: Paper/Pencil Problems
335 and 345 are doable

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Re: Paper/Pencil Problems
Problem 172 can be done by hand.(As shown in the private forum.)

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Re: Paper/Pencil Problems
#31 and #72 I did by pencil and paper. Does this mean I'm a computer? o.O
Re: Paper/Pencil Problems
I solved 43 by hand , So it too can be added to the list
http://projecteuler.net/problem=43
http://projecteuler.net/problem=43
Re: Paper/Pencil Problems
Problem 188 (View Problem). Nice to stumble on one after a yearlong hiatus.
And Arancaytar mentioned solving Problem 282 (View Problem) on paper.
And Arancaytar mentioned solving Problem 282 (View Problem) on paper.

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Re: Paper/Pencil Problems
Hi garethrees,garethrees wrote:Here are some that I think are solvable using paper and pencil:
Problem 1 — basic summation
Problem 2 — journeyman summation (Concrete Mathematics has a good chapter on this type of problem)
Problem 5 — easy
Problem 6 — more summation
Problem 8 — by inspection, if your eyesight is good!
Problem 15 — find the formula
Problem 17 — find the formula
Problem 18 — tedious, but only 120 steps, and the arithmetic is easier
Problem 19 — a very rough estimate might work out, you never know...
Problem 24 — much like long division
Problem 25 — might need a calculator once you've worked out the formula
Problem 26 — only need to examine a few cases, though the long division will be very tedious
Problem 28 — summation again
Problem 40 — easy
Problem 63 — only a few cases to check
Problem 69 — obvious once you see it
Problem 76 — just about doable, I think, with a Grundy scale (cf. Winning Ways)
Problem 79 — easier to do by hand than by computer!
Problem 85 — just about doable with the right formula and a good search strategy
Problem 97 — if you don't mind a lot of tedious multiplication (and you've read section 4.6.3 of The Art of Computer Programming!)
great solutions, i may use of these on my class ad i think it can be a good for me as a teacher,
thanks alot che
Re: Paper/Pencil Problems
Problem 190 (View Problem)
 Rainy Monday
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Re: Paper/Pencil Problems
Problem 169 (View Problem) with the right formula.
Re: Paper/Pencil Problems
Interesting that I just recently revisited this problem to remove my use of BigInteger; it didn't occur to me.Rainy Monday wrote:Problem 169 (View Problem) with the right formula.
Re: Paper/Pencil Problems
Problem 182 (View Problem)  reminiscent of P001
 Rainy Monday
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Re: Paper/Pencil Problems
#336 seems to be one.