Can't sleep?

Listen to Bertrand Russels's Introduction to Mathematical Philosophy.

You probably still won't fall asleep, but it's more productive and it beats counting sheep...

Solving a Non-Problem

If you solve Euler Project problem 26, you will be able to see my 'solution' in the forum for that problem on page 9, as user Gabriela.

It's terrible.  Taarrrribbble.   First I didn't research the math, thinking: Oh, that is _easy_!  Then one simple hack led to another quick hack (with a bit of faerydust sprinkled) and let's just say I got the correct solution the first time I checked, because I lucked out, not because I wrote a good algorithm.

Valgrind was happy with it.  I'm not.  After posting the code, I realised that *somehow* I crammed nearly 1000 chars into a string I malloc(500)'ed.

The question is:  Why did it work?  The next question is: would it work on another computer?  And most important of all: should it have worked in the first place?  Plus, other than eye balling the code and seeing the obvious problem, is there a way to check?

True, you could say that it's not a bug as such, because it does what I intended, but... the issue that I have, is if that isn't picked up with a nice helpful (and popular!) SIGSEV, what else is as dodgy and wrong?

Adding -fstack-protector-all didn't help to find a indication of an error either.

After some surfing, I found that dmesg (and readelf -s) is my friend, and, lo and behold:

(...)
[12556151.546186] project2-exe[18950]: segfault at 7fff5a18ae00 ip 00007fd452916744 sp 00007fffaddf9338 error 4 in libc-2.19.so[7fd45288d000+1bb000]                                                                       
[12564217.667780] traps: project2-exe[19250] general protection ip:7f94a50ad7cd sp:7fff01927b90 error:0 in libc-2.19.so[7f94a5072000+1bb000]
(...)         

Luckily I knew where the problem was, or so I thought.  But, alas, this was a previous SIGSEV which I had fixed[1] and there was nothing that readelf had to tell me.  After some more coffee, I finally had the bright idea that perhaps those allocations were just not used, and I checked the man pages for strndup() and strstr() and... yep, that was the non-problem.

[1] One good reason to use the emacs shell instead of M-x compile:  search upwards is trivial and you find out some things that otherwise would have confuzzled you for yonks.

I am now part of the 15.75%

... of members of Project Euler who have solved 25 coding problems and reached Level 1. (yay!)

But hang on, only less than 16% made it?  I think we should and can do better! So, join up and be entertained with quality puzzles.  How to solve?  Well, take a lesson from 'Transformer Owl':

Shlemiel, the painter

A friend sent me this delightful joke which also doubles up as a puzzle, after I complained that the more I study, the longer my to-do list gets.

 (Go on, solve it, you know you want to.)

Personally, I think this was the best comment:

"You do realize, we're trying to sum up Stupidity as a Mathematical Equation."

But I also like the big collection of possible approaches --- those solutions have everything!

My solution is here, hidden as blue text on blue background:

Shlemiel can walk M meters per day, and his effort can be modelled as an Arithmetic series S_n  with the points S_x, S_y and S_z, therein, so we're looking for M = S_x,  2M = S_y and 3M = S_z and the values of x, y and z which give us the total distance reached on each day.

Rearranging S_n = n/2 (2p + d(n+1)) we get 2 S_n = dn^2 + dn +2pn = [(2S_n - 2pn) / d ] - n = n^2. 

(where p is the initial length and d is the distance) 

There is no closed form for finding n, but because n^2 is the biggest term, we can simply ignore the others and extract our values for x, y and z thus: 

x = floor(sqrt(M)), y = floor(sqrt(2M)) and finally, z = floor(sqrt(3M)).

On day one he paints a = x meters, the next day he manages b = (y - a) meters, and finally, c = (z - b) meters on the third. 

Update: there is of course always at least one error in every solution... and the above is no exception :) 

So...

x = floor(sqrt(2 M/d)), y = floor(sqrt(2*2M/d)) and finally, z = floor(sqrt(2*3M/d)).

Moral of the story: beware of working with convenient values.

Productive Procrastination

I rediscovered my old math grind bible -- Engineering Mathematics by K. Stroud.

It's not a math course as such, more like a collection of sure-fire 'how do I calculate ...' recipes and a decent amount of exercises for every topic with answers.


So, I'm working through this book instead of playing Sudoku every time need a short puzzle break --- of course it's still procrastination, but, it feels a lot more productive!