## Paper/Pencil Problems

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idantlol
Posts: 16
Joined: Mon Jul 11, 2011 12:14 pm

### 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.

Francky
Posts: 90
Joined: Sat May 07, 2011 2:49 pm
Location: South of France

### Re: Paper/Pencil Problems

PE197, first time by dBlade 10 Jun 2008 10:45 am.
Entia non sunt multiplicanda praeter necessitatem

hk
Posts: 10202
Joined: Sun Mar 26, 2006 9:34 am
Location: Haren, Netherlands

### Re: Paper/Pencil Problems

Francky wrote:PE197, first time by dBlade 10 Jun 2008 10:45 am.
That's no pencil and paper but calculator and thumb. (pun intended).

Francky
Posts: 90
Joined: Sat May 07, 2011 2:49 pm
Location: South of France

### Re: Paper/Pencil Problems

hk wrote:
Francky wrote:PE197, first time by dBlade 10 Jun 2008 10:45 am.
That's no pencil and paper but calculator and thumb. (pun intended).
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.
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
Posts: 10
Joined: Mon Sep 12, 2011 5:06 am
Location: Costa Rica

### 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 )

-- I play Baduk at online-go --

Rainy Monday
Posts: 18
Joined: Sun Sep 25, 2011 2:55 pm

### Re: Paper/Pencil Problems

I'd say Problem 33 (View Problem) is a fine example too.

Fogmeister
Posts: 27
Joined: Mon Aug 22, 2011 10:20 am

### 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.

PurpleBlu3s
Posts: 73
Joined: Mon Sep 19, 2011 5:49 pm

### 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.

Eternalcode
Posts: 12
Joined: Mon Oct 03, 2011 1:25 am
Location: California, USA

### Re: Paper/Pencil Problems

You can also solve 205 with a pencil and paper.

Marcus_Andrews
Posts: 1444
Joined: Wed Nov 09, 2011 5:23 pm

### Re: Paper/Pencil Problems

335 and 345 are doable

Eternalcode
Posts: 12
Joined: Mon Oct 03, 2011 1:25 am
Location: California, USA

### Re: Paper/Pencil Problems

Problem 172 can be done by hand.(As shown in the private forum.)

dianopoulos
Posts: 1
Joined: Mon Oct 15, 2012 1:21 am

### Re: Paper/Pencil Problems

#31 and #72 I did by pencil and paper. Does this mean I'm a computer? o.O

Gnomy
Posts: 1
Joined: Fri May 31, 2013 10:29 am

### Re: Paper/Pencil Problems

I solved 43 by hand , So it too can be added to the list
http://projecteuler.net/problem=43

GenePeer
Posts: 112
Joined: Sat Apr 03, 2010 12:14 pm
Contact:

### Re: Paper/Pencil Problems

Problem 188 (View Problem). Nice to stumble on one after a year-long hiatus.

And Arancaytar mentioned solving Problem 282 (View Problem) on paper.

chekellog1010
Posts: 1
Joined: Fri Jun 28, 2013 8:01 am

### Re: Paper/Pencil Problems

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!)
Hi garethrees,
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

GenePeer
Posts: 112
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### Re: Paper/Pencil Problems

Problem 190 (View Problem)

Rainy Monday
Posts: 18
Joined: Sun Sep 25, 2011 2:55 pm

### Re: Paper/Pencil Problems

Problem 169 (View Problem) with the right formula.

GenePeer
Posts: 112
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### Re: Paper/Pencil Problems

Rainy Monday wrote:Problem 169 (View Problem) with the right formula.
Interesting that I just recently revisited this problem to remove my use of BigInteger; it didn't occur to me.

GenePeer
Posts: 112
Joined: Sat Apr 03, 2010 12:14 pm
Contact:

### Re: Paper/Pencil Problems

Problem 182 (View Problem) - reminiscent of P001

Rainy Monday
Posts: 18
Joined: Sun Sep 25, 2011 2:55 pm

### Re: Paper/Pencil Problems

#336 seems to be one.