A place to share links to other websites and interesting articles
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.
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
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.
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