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brute force effectiveness threshold =

Personally I love programming and although I've never been in a chair since I started programming computers have troubled me for making my pc run my creative ideas with the collaboration of a person (Jorge Ardila) met the schedule and with the help of a lot of creativity and a bit of reading I managed to do very interesting things within those things my undergraduate thesis (an application of Matlab for the study of conics), plus I joined the Project Euler is a very interesting challenge for those of us in the algorithm. The fact is that after years programming in my own way (sitting in front of the pc more than an idea without a language and a couple of books) the Euler project has taught me that it is better to start thinking about the idea and creativity not only exploit but the algorithm generated other ideas, in particular, last night to face the Euler Project Problem 25 I found a surprise. Resa Problem 25 (in summary):

The tenth second term in the Fibonacci series is the first to have three digits, and the question is which is the first term of the series that has 1000 digits.

As usual, with the clear objective I sat opposite to my super computer and I started thinking about how to achieve the goal, my first thought was to lay down one by one each term of the Fibonacci series and count how many digits each term has so that the program would end when you find the first term of 1000 digits, so I did, a few lines of code, a couple of tests and everything was ready, I started doing walking, I saw that it took too long but I stopped because I knew my other algorithms have been taken up to two hours to find the answer, but reached a point where my intuition more than my impatience led me to stop process, and go off to rest.

Today when I wake up first thing I did was sit back with my super friend and start breaking down what was happening, I began to test my algorithm gradually increasing the number of digits 100, 200, 300, 400 and started late, I stopped because I knew that the beginning of the delay was between 300 and 400, new test at 350 and nothing (demora. ..), then started increasing digit by digit from 300, 301, 302, ... 309 and all good but ... at 310, delay. Well, I decided to make the calculation of the term with 310 digits to pedal, then take the general form of the Fibonacci series and looked for calculating the first term with 310 digits, INF response, ie after the end with 309 digits, the sum is too large to be calculated, that means ups think of another way to tackle the problem.

then I started making a list of items from the number of digits and I found the feature that allowed me to determine my model. The thing is, determining the number of digits that must have a term specific Fibonnacci series can be determined that the first term to have one digit more than the previous 5 positions below this for example the term with 9 digits is at position 40 and 10-digit term is in position 45 However, each 5-digit increases only four positions, ie the term 14 is in position 64, after that term again adding 5 positions for each digit, but curiosity can be more easily seen in the table below


Position 28 131

	# Digit Position # Digits
9	40	29	136
10	45	30	141
11	50	31	146
12	55	32	151
13	60	33	155
14	64	34	160
15	69	35	165
16	74	36	170
17	79	37	174
18	84	+5=42	+24=198
19	88	+5=47	+24=222
20	93	+4=51	+19=241
21	98	+10=61	+48=289
22	103	+4=65	+19=308
23	107	+14=79	+67=375
24	112	+28=107	+134=509
25	117	+28=135	+134=643
26	122
27 127

then I found some patterns that allow modeling the behavior of the Fibonacci series with respect to at least number of digits of each term, the model is: the first five digits are the previous positions twenty-four forward, but every fourteen digits, only four positions increases which leads us to create a model in which every 28 134 positions digit increases.

This was very easy to make a script which could find the first term to have more than 1000 digits (1003) and the first being close to a thousand digits but below a thousand (975), with this and the application logic of the model found it was easy and fast response.

CONCLUSION: Sometimes
worth thinking about the question on how to answer it.

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Matlab problems to solve large products

Solve Euler project has become a daily habit and more to discover that we advance in the list the problems get more and more interesting, however there are some really simple solution, the question is to give the best look to avoid a brute force algorithm that consumes too much processing time when not strictly necessary (although this type of algorithm is good to create them because they leave open the interesting code changes).

However, although he continued to solve problems, today I want to say something very interesting that met yesterday to attempt to resolve the problem 20 proposed to determine the sum of all digits of the 100!, Really easy to work and that using num2str function and its inverse str2num can build a string vector with the vectors and add all the entries in this vector, the error appeared to get the final result because it does not coincide with that calculated on my calculator (Texas Instruments Voyage 200).

After a rigorous treatment of the issue found that:

Texas Instruments Voyage 300 Net operating

50 * 49 * 48 * 47 * 46 * 45 * 44 * 43 * 42 * 41 * 40 * 58150627116341760000 39
is

Matlab R2008b (GNU / Linux Debian Squeeze)
the same operation results
58150627116341755904

and from 39, the factor of 100 change with respect to the results obtained in calculator as a pedal (manual check done).

Explanation?? I wish I had answers
.

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Two hours of processing for a number

The problem or Collatz Conjecture, a problem proposed by the mathematician Lothar Collatz in 1937 and has not yet been shown, generates a series of whole numbers is always presumed that ends in one, approach says that if n is even the new term is n / 2, where 3n +1 is odd, so for example with the entire first 13, the series will

13 to 40 - 20 - 10 - 5 to 16 - 8 - 4 - 2 -1

The problem proposed in the draft to find the entire Euler indicates less than a million producing the longest Collatz chain, this implies in the script that I developed to calculate Collatz chain with all the integers less than 1000000 and determine each of those million channels, few elements have, so after just over two hours I dropped the response process, the longest string that is generated with an integer less than a million contains 525 items, the question concerned at what the original whole that generates that string, the answer can be found running the following script in matlab ;-)


clc;
clear all;
i = 2, j = 1;
k = input ('Enter the initial maximum value k =');
while k ~ = 1
n = k;
 c(1)=n;
    while n~=1
        if rem(n,2)~=0
            n=3*n+1;
        elseif rem(n,2)==0
            n=n/2;
        end
        c(i)=n; % Vector containing the full chain including the initial term if

n ~ = 1 i = i +1;% Indisa the terms of the chain

elseif n == 1 i = 2;
end end

m1 (j, 1) = c (1);% Vector of initial values \u200b\u200bof the chain
m2 (j, 1) = length (c);% Vector of the number of terms each string
M = [m1 m2];
clear c;
j = j +1, k = k-
1;

end disp (m1 (find (m2 == max (m2)), 1));


PDTA: This algorithm makes it equivalent to a brute force attack because it determines each of the chains Collatz The most practical way to resolve reduce running time Collatz function built into Matlab .

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Project Euler Problem 14 Project Euler - Problem interesting !?!?!

So far, spend the time and moments with the coding to solve the issues raised by the Project Euler has been a task of immense satisfaction especially as outstanding challenges posed by new concepts of concern and knowledge, but some of these issues have some seem tasteless when asked to get out of step, it is even more offensive to be problematic as meaningless, example is the problem for its development 13 that more time is taken squalid enter 100 numbers of 50 digits each, which means add them all to know what the first ten digits of this result. I personally prefer

problems involving the generation script's to find results with special features such as the problem 12 in the calling discover the first triangular number is over five hundred divisors.

But anyway, the problems have already been written and there is no way I leave I generated script to solve the problem 12, this script should be improved to be more precise execution but as this achieves the goal. Find

% triangular numbers, including triangular numbers (in
% this case) has more than 501 divisors, to improve when you find the first
% the condition stops.
d = (1:1000000) 1:1000000

for n = T = n * (n +1) / 2;
p = find (rem (T, d) == 0);
if length (d (p))> = 501
disp (T);
; disp (length (d (p)));

end end


So far they are determined 12 of the 13 problems where I worked because the problem 11 asked to teach the computer to solve puzzles with 20x20 matrix, solve that problem will be sublime jejeje.

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Al-Hakim-Demo (1998) and Shadow Sooul

Al-Hakim, made by Moopy Pro in the production and MC's Arthur (under the pseudonym El Puto Mazo), the sisters La Primera and La Nana, LNita and DieMeis (now known as Eleme One), gave us this great band in February 1998 showing that the rap of Cordoba would remain at the forefront after the dissolution of his group germ, the legendary 957 Kolt. The band performed in many concerts in the south of the country until LNita left the project and changed its name to 4x4. With such training, the band would continue to act until its dissolution in 2000 leaving a mini-cd recorded 6 song self-titled recorded in Superior Records. Today, Eleme One, located in Malaga, continues his work managing Pussy Clap Productions with 137 and Solitary Cio, where he has recently published and born and breeding work mixtape format where it appears among other collaborators El Puto Mazo.

01 - blow verbal

02 - We think

05 - Under the law

06 - Simple and direct

07 - Checkmate

08 - The flowers of Al-Hakim

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presented Kioltape 2000 (2001)

The renowned producer and DJ Terrassa Giro er Nene, formerly known as Kiol, took his first steps as an MC in 1989 and later Permanent Vado group in 21 with Zenia (now known as Tremendo). In 2000 he began to emerge nationally in his role as producer to appear on the discs A2Velas, Dobleache and the second album of remixes of La Puta OPP. This wonderful film saw the light and was distributed in 2001 as a promotional gift by type stores nationwide next to the debut album by Payo Malo "With land in the pockets', released on the label and produced almost Avoid entirely by our protagonist. It showed a good example of scratch's own productions and Giro, Juan Pro and Pitch Control Pin is the voice that put a good selection of MC's from around the country as Ari, El Puto Coke, Kase.O, Double H and Great people.

01 - Payo Malo "The night (mixtape version)
02 - Great People" From one end to the 1998
03 - "A big issue Nomah
04 - Intro 1999
Arizona 05 - Arizona quiet and listen
06 - Double H" When the illusion does not sell
07 - Dilemma "You're not going to get
08 - Kiko G Without AKA - My early
09 - As many as two-way
flowed 10 - Pin is Pitch Control-The Adventures of ...
11 - Grand Village (+ Juan Pro) - We put in on!
12 - El Puto Coke "In 41 minutes
13 - Kase.O-Again improvising
14 - A2V (+ El Barbas) - Second time
15 - Marra
Funkarra-Genesis 16 - The Sixth People-Things are well
17 - John the Deep-The two pearls
18 - El Rubio (+ Juan Pro) - Funkinkis
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Solutions (Project Euler and others)

After a long absence Mauripides becomes active first trouble connecting to the internet (thank God and solved) and second a challenge to correctly interpret what the seventh issue of the Project Euler proposed the original question here

Find the greatest product of five consecutive digits in the number of 1000 digits

73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586

17866458359124566529476545682848912883142607690042 24219022671055626321111109370544217506941658960408 07198403850962455444362981230987879927244284909188


84580156166097919133875499200524063689912560717606 05886116467109405077541002256983155200055935729725 71636269561882670428252483600823257530420752963450

What many may become apparent to me took several days to understand, this is the correct interpretation

In 1000 the number of digits, select quintublas of adjacent digits and these quintuplets to find the largest product of five digits.

For after to achieve this performance (support included), to develop the algorithm that was resolved some just seconds


n = [7 3 1 6 7 1 7 6 5 3 1 3 3 0 6 2 4 9 1 9 2 2 5 1 1 9 ... 0];% Vector with the 1000 digit
i = 1, j = 5;
while j \u0026lt;= 1000
r (j) = prod (n ( i, j));% Creates a vector which stores all the products of consecutive digits quintublas
i = i +1, j = j +1; end
;
disp (max (r)),% print the maximum of consecutive digits quintublas

On the other hand, after resolving connection problems, go ahead and Culture Universe Alcuerno by RadioGNU and other Mauripides project, others are preparing for the book Notes from Trigonometry and Geometry Analytics will be released under creative commons license.

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E1MD-Recordings (1998)

LGS

The collective (The Thugs), formed by b-boys and graffiti writers from Madrid, Paracuellos del Jarama, La Alameda de Osuna, Barrio de la Concepción, La Elipa and Manuel Becerra in the mid-90, gave birth to the first bands of some of the most notable artists of the Madrid scene today as High Gambino, Latex Diamond, Truth or Zeki Sholo. E1MD (in 1 time) was a band created in 1997 by Kiba, who came from a short-lived formations called Narcotyk LHB and Crew with Mine (now Mitsuruggy) and Koma (High Gambino) after passing through 4 Insane with Seker (Latex Diamond), Zeki and Nano (grouped under the name of the entry Pidaras Glaxo and DJ Kaze, now known as Sholo Truth). This film contains some home recordings of the duo produced by Koma himself (except the track 05 produced by Kaze, who alternated his work in live DJ in the group) and showed the good form of its components years before the creation of The collective Traga'M (Latex Diamond, Sholo Truth, Kiba and Mitsuruggy) in 1999, the group LaCalle family (headed by High Gambino after his stay in London) and the current independent label Uglyworkz.

01 - No Way Out
02 - Thugs
03 - Always present
04 - Love of My Life (Intro)
05 - The love of my life
06 - Freestyle in
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On Saturday December 4th Workshop Family Constellation had. A day called FAMILY. Was the workshop with which I close the group activities in 2010 and was a gift not only for the participants, but where we work.

Some of the most important ideas that I'm of work yesterday, I can be summarized as follows:

* The importance of agreeing and acknowledging what it is. When it is motivated by anger and resentment, we see what it is, the facts as they are, we engaged with the childish idea of \u200b\u200bwanting to change what we dislike, which do not accept and what hurts us.

* The best way to honor our beloved dead in embracing life with strength and nodding to their destinations and to ours with the same force. We do nothing if we do not accept this pain. That's when someone in our system, sees the pain for us, for example our children.

* The soul knows more than our thoughts and our minds. The soul knows what it needs, what hurts, what you need. So just think of what participants say and then leave it to the system that report what happens "in the truth." It is a wonder to be awed by the system.

* Sometimes we engage in to achieve a specific goal and not on the resources needed to achieve this or that goal. Yesterday work showed us how when we focus on potential and actual resources, my relationship with the target can be better, stronger and more accurate.

* Some conditions come to show us something. They are lessons. Sometimes, the real subject of the soul is not the disease itself, but how we handle it, so who is sick and who is at his side. Many times, trust, let go, do little or nothing, may be a better way to be, for all involved.

* There is little I can do for the prosperity of another. In any case I can take care of myself and look with love and honor the other's destiny. Everyone in their place.

* The system is so great, so wise and shows the truth that even decide to stop a job, the same issue could arise again to look at why we need to look. Just have to trust. Once I can look with love to my family, I am more available for my partner.

a day is difficult to summarize in a few lines ... because what happens in a workshop is always bigger than all that we are there and participate.
I can only thank my people, my teachers, this powerful force I moves from the soul to continue this work, each of the participants who will lovingly and delivered. Thanks a lot! Raiza Ramirez

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Other problems already solved - Project Euler Palindromes

After finding the solution to the problem of palindromes, (which he think) the fifth was also very interesting problem to solve but comfortable, the most interesting of this problem is so such as palindromes, the generated script allows you to test the processing power of the machine, the fifth problem, my laptop took 28 minutes to throw a response as my desktop only took 8 minutes to get to devote only one of its four cores.

The problem is to find the smallest positive number that is divisible by all the natural range of 1 to 20, the answer is 232792560.

The script was generated to achieve the following

% Find the smallest number that is divisible by all the series and to n

% n = input ('Enter the number of splitters');% initial dividend
d = (1: n) % Vector of divisors
r = rem (n, d);% of the remaining vector
while any (r) == 1% if any of the remaining non-zero
n = n +1 ;% new dividing
r = rem (n, d);

end if r == 0% if all remnants are zero
disp (n);
disp (r);

end

After this problem appeared one that is very easy to fix. Find the difference between the sum of the squares of the first 100 natural and the square of the sum of the first 100 natural. 25164150 Response. For this problem is not necessary to generate any script, simply create a natural vector of one (1) to twenty (20) and use the SUM function.

N = (1:20)% generates a natural vector of 1 to 20
d = sum (N ^ 2) - (sum (N)) ^ 2

and that's it. The next problem is also very simple to solve. Ask to meet the prime number 10001, that by using the primes is in a couple of seconds.

I still addressing the problems of the Euler Project, I pair the eighth problem.