## Paper/Pencil Problems

A place to air possible concerns or difficulties in understanding ProjectEuler problems. This forum is not meant to publish solutions. This forum is NOT meant to discuss solution methods or giving hints how a problem can be solved.
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### Paper/Pencil Problems

I'm trying to improve my mathematics skills. I'm already learning a great deal from some problems and I would like to know the problems that can be solved by Paper/Pencil.

Edit: I decided to add the problems here in order. I will continue to post them normally as it seems people only post after I post and the thread is back at the top of the forum.

Paper/Pencil Problems suggested:
Problem 1 (View Problem)
Problem 2 (View Problem)
Problem 4 (View Problem)
Problem 5 (View Problem)
Problem 6 (View Problem)
Problem 8 (View Problem)
Problem 9 (View Problem)
Problem 15 (View Problem)
Problem 17 (View Problem)
Problem 18 (View Problem)
Problem 19 (View Problem)
Problem 24 (View Problem)
Problem 25 (View Problem)
Problem 26 (View Problem)
Problem 28 (View Problem)
Problem 29 (View Problem)
Problem 31 (View Problem)
Problem 33 (View Problem)
Problem 38 (View Problem)
Problem 40 (View Problem)
Problem 43 (View Problem)
Problem 45 (View Problem)
Problem 59 (View Problem)
Problem 63 (View Problem)
Problem 68 (View Problem)
Problem 69 (View Problem)
Problem 71 (View Problem)
Problem 72 (View Problem)
Problem 76 (View Problem)
Problem 79 (View Problem)
Problem 84 (View Problem)
Problem 85 (View Problem)
Problem 94 (View Problem)
Problem 96 (View Problem)
Problem 97 (View Problem)
Problem 100 (View Problem)
Problem 108 (View Problem)
Problem 110 (View Problem)
Problem 112 (View Problem)
Problem 113 (View Problem)
Problem 114 (View Problem)
Problem 115 (View Problem)
Problem 116 (View Problem)
Problem 117 (View Problem)
Problem 120 (View Problem)
Problem 121 (View Problem)
Problem 138 (View Problem)
Problem 139 (View Problem)
Problem 142 (View Problem) (by Rolle & Euler )
Problem 145 (View Problem)
Problem 147 (View Problem)
Problem 148 (View Problem)
Problem 158 (View Problem)
Problem 162 (View Problem)
Problem 168 (View Problem)
Problem 169 (View Problem)
Problem 172 (View Problem)
Problem 175 (View Problem)
Problem 176 (View Problem)
Problem 182 (View Problem)
Problem 188 (View Problem)
Problem 190 (View Problem)
Problem 194 (View Problem)
Problem 202 (View Problem)
Problem 205 (View Problem)
Problem 207 (View Problem)
Problem 208 (View Problem)
Problem 218 (View Problem)
Problem 241 (View Problem)
Problem 282 (View Problem)
Problem 301 (View Problem)
Problem 317 (View Problem)
Problem 335 (View Problem)
Problem 336 (View Problem)
Problem 345 (View Problem)

Note: I include questions that can be simplified to a single expression that needs to be evaluated by a calculator/WolframAlpha.

Thanks for the suggestions.
Last edited by GenePeer on Sat Jun 21, 2014 6:49 pm, edited 33 times in total.

GenePeer

Posts: 111
Joined: Sat Apr 03, 2010 12:14 pm

### Re: Paper/Pencil Problems

There are alot that can be done by pen and paper, if you know alot about math and are creative with it .

Don't know which problems you've already tackled, but problem 29 was really fun to do with pen and paper.
Allasar

Posts: 4
Joined: Fri Jul 30, 2010 1:05 pm

### Re: Paper/Pencil Problems

Problem 5 is actually really easy to do with pencil and paper. In fact...I've done every number for up to 83...took a whiteboard though...
Want some
3.14159265358979323846264338327950288419716939937510
58209749445923078164062862089986280348253421170679...?

elendiastarman

Posts: 410
Joined: Sat Dec 22, 2007 8:15 pm

### Re: Paper/Pencil Problems

i have solved problem 79 using keyboard & notepad
so i guess you can solve it too using paper & pencil
elr

Posts: 69
Joined: Thu Apr 09, 2009 8:47 am

### Re: Paper/Pencil Problems

Problem 158 yields an algebraic answer to pencil and paper, though calculating the final answer takes a high-precision calculator
rmillika

Posts: 39
Joined: Thu Apr 05, 2007 3:37 pm

### Re: Paper/Pencil Problems

#24 needs a bit of logic but then is easy in P/P. Try it first on the 24 perms of 1,2,3,4
#96 50 Soduku !! not all on one day though.
#59 get the key with logic, then manually convert the decimals to binary, do the XOR, but then the hard part is adding the ASCII values. Count the number of "a"s, "b"s etc, then * by its value. Betcha get it wrong.!
whakamaru

Posts: 47
Joined: Thu May 06, 2010 10:08 pm

### Re: Paper/Pencil Problems

Allasar wrote:There are alot that can be done by pen and paper, if you know alot about math and are creative with it .

Don't know which problems you've already tackled, but problem 29 was really fun to do with pen and paper.

Oh...i just couldn't solve problem29 using anyway...Frustrating.

but anyway i know there's sth related to prime factors...
allenfantasy

Posts: 2
Joined: Mon Feb 15, 2010 1:04 pm

### Re: Paper/Pencil Problems

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!)
Last edited by garethrees on Wed Sep 08, 2010 11:27 am, edited 1 time in total.
garethrees

Posts: 7
Joined: Fri Sep 03, 2010 11:19 am

### Re: Paper/Pencil Problems

garethrees wrote:Problem 97 — if you don't mind a lot of tedious multiplication

Hk pencil/papered #108 >.<

hjaya

Posts: 5
Joined: Mon Aug 17, 2009 6:30 am
Location: Indonesia

### Re: Paper/Pencil Problems

Ha, those were times.

hk

Posts: 8108
Joined: Sun Mar 26, 2006 9:34 am
Location: Haren, Netherlands

### Re: Paper/Pencil Problems

hjaya wrote:
garethrees wrote:Problem 97 — if you don't mind a lot of tedious multiplication

Hk pencil/papered #108 >.<

Me too. I think it is feasible to solve 110 with pencil and paper too.
Quique12

Posts: 7
Joined: Sun Sep 05, 2010 6:08 am

### Re: Paper/Pencil Problems

Problem 71 can be solved without a computer as well, though I can't remember how I did it exactly.
Frigo

Posts: 4
Joined: Sun Aug 22, 2010 10:54 am

### Re: Paper/Pencil Problems

For a lot of problems you can find a direct formula that allows you to calculate the answer with paper/pencil. However finding that direct formula usually required me some pattern spotting on bruteforce results, so I did use a computer anyhow..

Problem 194 (View Problem) is a reasonably difficult problem that can be solve with just pencil and paper.

stijn263

Posts: 1505
Joined: Sat Sep 15, 2007 10:57 pm
Location: Netherlands

### Re: Paper/Pencil Problems

Thanks for the suggestions people. I've done some (just finished P15, required an "AHA" moment) and feeling proud of myself. Now on the Fibonacci questions.

garethrees wrote:Problem 17 — find the formula

Is that even possible? Formula for letters in a number?

GenePeer

Posts: 111
Joined: Sat Apr 03, 2010 12:14 pm

### Re: Paper/Pencil Problems

hjaya wrote:Hk pencil/papered #108 >.<

After reading his explanation in #108, I did #110 by hand and phone calculator.

Problem 84 (View Problem) If you don't mind doing tedious multiplications.
Last edited by GenePeer on Thu Feb 03, 2011 11:36 pm, edited 1 time in total.

GenePeer

Posts: 111
Joined: Sat Apr 03, 2010 12:14 pm

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