Paper/Pencil Problems

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Paper/Pencil Problems

Postby GenePeer » Sun Aug 15, 2010 12:56 pm

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:
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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.
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Re: Paper/Pencil Problems

Postby Allasar » Mon Aug 16, 2010 1:57 pm

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.
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Re: Paper/Pencil Problems

Postby elendiastarman » Mon Aug 16, 2010 2:11 pm

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... :P
Want some
3.14159265358979323846264338327950288419716939937510
58209749445923078164062862089986280348253421170679...?
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Re: Paper/Pencil Problems

Postby elr » Mon Aug 16, 2010 3:15 pm

i have solved problem 79 using keyboard & notepad :)
so i guess you can solve it too using paper & pencil
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Re: Paper/Pencil Problems

Postby rmillika » Mon Aug 16, 2010 5:55 pm

Problem 158 yields an algebraic answer to pencil and paper, though calculating the final answer takes a high-precision calculator
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Re: Paper/Pencil Problems

Postby whakamaru » Thu Aug 19, 2010 11:02 pm

#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.!
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Re: Paper/Pencil Problems

Postby allenfantasy » Sat Aug 28, 2010 10:25 am

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...
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Re: Paper/Pencil Problems

Postby garethrees » Fri Sep 03, 2010 11:57 am

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.
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Re: Paper/Pencil Problems

Postby hjaya » Mon Sep 06, 2010 12:14 pm

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

Hk pencil/papered #108 >.<
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Re: Paper/Pencil Problems

Postby hk » Mon Sep 06, 2010 2:05 pm

Ha, those were times. :roll:
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Re: Paper/Pencil Problems

Postby Quique12 » Tue Sep 07, 2010 5:20 am

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.
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Re: Paper/Pencil Problems

Postby Frigo » Thu Sep 16, 2010 4:38 pm

Problem 71 can be solved without a computer as well, though I can't remember how I did it exactly.
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Re: Paper/Pencil Problems

Postby stijn263 » Sat Sep 18, 2010 8:02 pm

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 {TEXT} (View Problem) is a reasonably difficult problem that can be solve with just pencil and paper.
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Re: Paper/Pencil Problems

Postby GenePeer » Sun Sep 26, 2010 6:57 pm

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? :?
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Re: Paper/Pencil Problems

Postby GenePeer » Wed Jan 26, 2011 11:28 am

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

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

Problem {TEXT} (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.
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