Solutions to lace1

lace1_solutions.txt

Question 1
Fibonacci series are defined as the number in the following integer sequence  0,1,1,2,3,5,8,13,21,34,55,89,144 <br>

Let there be a function such that f(0,1) which generates the fibonacci series, where 0,1 are the first two terms of the fibonacci series.
such that f(4,5) will generate the following series 4,5,9,14,23,37,60 ... <br>
Find the 20th term of the series represented f(100,101)

ANS 1101365

Solution:

#include<stdio.h>

long int gib(long int n){
	if(n==0)	return 100;
	if(n==1)	return 101;
	else	return gib(n-1) + gib(n-2);

}

int main(){
	char c;
	int i=0;
	
	for(i=0;i<=20;i++){
		printf("%lu\n",gib(i));
	}
	
        c=getchar();
	return 0;

}

==========================================================================================================================
QUESTION 2:
Adventures of Huckleberry Finn is an excellent book by Mark Twain about a little boy named Huckleberry Finn.
Find the number of lines (L), number of words (W) and number of characters (C) in the online version of the book 
<a href="http://www.gutenberg.org/files/76/76.txt">http://www.gutenberg.org/files/76/76.txt</a>.
<br>
Find L+W+C
Hint: words are defined as a body of text having space on both ends, even standalone characters like a,I,; should be counted as words.

!*ANS*!	732174

SOLUTION: (in python for ease in fileIO)
fname = "76.txt"

num_lines = 0
num_words = 0
num_chars = 0

with open(fname, 'r') as f:
    for line in f:
        words = line.split()

        num_lines += 1
        num_words += len(words)
        num_chars += len(line)

print num_lines+ num_words + num_chars

=============================================================================================================================

QUESTION 3:
There must be a character which would be occurring most frequently in <a href="http://www.gutenberg.org/files/76/76.txt"> Adventures of Huckleberry Finn</a>, how many times does this character occur in this file ?
only consider alphabets and numbers as characters.

!*ANS*! 49264

SOLUTION: (again in python)

content = open("76.txt").read()
print content.count('a')

max=0;


for i in 'abcdefghijklmnopqrstuvwxyz1234567890':
    if content.count(i) > max:
        max= content.count(i)
        c=i

print max




==============================================================================================================================

QUESTION 4:
Work out the first five digits of the sum of the following one-hundred 50-digit numbers.

37107287533902102798797998220837590246510135740250<br>
46376937677490009712648124896970078050417018260538<br>
74324986199524741059474233309513058123726617309629<br>
91942213363574161572522430563301811072406154908250<br>
23067588207539346171171980310421047513778063246676<br>
89261670696623633820136378418383684178734361726757<br>
28112879812849979408065481931592621691275889832738<br>
44274228917432520321923589422876796487670272189318<br>
47451445736001306439091167216856844588711603153276<br>
70386486105843025439939619828917593665686757934951<br>
62176457141856560629502157223196586755079324193331<br>
64906352462741904929101432445813822663347944758178<br>
92575867718337217661963751590579239728245598838407<br>
58203565325359399008402633568948830189458628227828<br>
80181199384826282014278194139940567587151170094390<br>
35398664372827112653829987240784473053190104293586<br>
86515506006295864861532075273371959191420517255829<br>
71693888707715466499115593487603532921714970056938<br>
54370070576826684624621495650076471787294438377604<br>
53282654108756828443191190634694037855217779295145<br>
36123272525000296071075082563815656710885258350721<br>
45876576172410976447339110607218265236877223636045<br>
17423706905851860660448207621209813287860733969412<br>
81142660418086830619328460811191061556940512689692<br>
51934325451728388641918047049293215058642563049483<br>
62467221648435076201727918039944693004732956340691<br>
15732444386908125794514089057706229429197107928209<br>
55037687525678773091862540744969844508330393682126<br>
18336384825330154686196124348767681297534375946515<br>
80386287592878490201521685554828717201219257766954<br>
78182833757993103614740356856449095527097864797581<br>
16726320100436897842553539920931837441497806860984<br>
48403098129077791799088218795327364475675590848030<br>
87086987551392711854517078544161852424320693150332<br>
59959406895756536782107074926966537676326235447210<br>
69793950679652694742597709739166693763042633987085<br>
41052684708299085211399427365734116182760315001271<br>
65378607361501080857009149939512557028198746004375<br>
35829035317434717326932123578154982629742552737307<br>
94953759765105305946966067683156574377167401875275<br>
88902802571733229619176668713819931811048770190271<br>
25267680276078003013678680992525463401061632866526<br>
36270218540497705585629946580636237993140746255962<br>
24074486908231174977792365466257246923322810917141<br>
91430288197103288597806669760892938638285025333403<br>
34413065578016127815921815005561868836468420090470<br>
23053081172816430487623791969842487255036638784583<br>
11487696932154902810424020138335124462181441773470<br>
63783299490636259666498587618221225225512486764533<br>
67720186971698544312419572409913959008952310058822<br>
95548255300263520781532296796249481641953868218774<br>
76085327132285723110424803456124867697064507995236<br>
37774242535411291684276865538926205024910326572967<br>
23701913275725675285653248258265463092207058596522<br>
29798860272258331913126375147341994889534765745501<br>
18495701454879288984856827726077713721403798879715<br>
38298203783031473527721580348144513491373226651381<br>
34829543829199918180278916522431027392251122869539<br>
40957953066405232632538044100059654939159879593635<br>
29746152185502371307642255121183693803580388584903<br>
41698116222072977186158236678424689157993532961922<br>
62467957194401269043877107275048102390895523597457<br>
23189706772547915061505504953922979530901129967519<br>
86188088225875314529584099251203829009407770775672<br>
11306739708304724483816533873502340845647058077308<br>
82959174767140363198008187129011875491310547126581<br>
97623331044818386269515456334926366572897563400500<br>
42846280183517070527831839425882145521227251250327<br>
55121603546981200581762165212827652751691296897789<br>
32238195734329339946437501907836945765883352399886<br>
75506164965184775180738168837861091527357929701337<br>
62177842752192623401942399639168044983993173312731<br>
32924185707147349566916674687634660915035914677504<br>
99518671430235219628894890102423325116913619626622<br>
73267460800591547471830798392868535206946944540724<br>
76841822524674417161514036427982273348055556214818<br>
97142617910342598647204516893989422179826088076852<br>
87783646182799346313767754307809363333018982642090<br>
10848802521674670883215120185883543223812876952786<br>
71329612474782464538636993009049310363619763878039<br>
62184073572399794223406235393808339651327408011116<br>
66627891981488087797941876876144230030984490851411<br>
60661826293682836764744779239180335110989069790714<br>
85786944089552990653640447425576083659976645795096<br>
66024396409905389607120198219976047599490197230297<br>
64913982680032973156037120041377903785566085089252<br>
16730939319872750275468906903707539413042652315011<br>
94809377245048795150954100921645863754710598436791<br>
78639167021187492431995700641917969777599028300699<br>
15368713711936614952811305876380278410754449733078<br>
40789923115535562561142322423255033685442488917353<br>
44889911501440648020369068063960672322193204149535<br>
41503128880339536053299340368006977710650566631954<br>
81234880673210146739058568557934581403627822703280<br>
82616570773948327592232845941706525094512325230608<br>
22918802058777319719839450180888072429661980811197<br>
77158542502016545090413245809786882778948721859617<br>
10107838435069186155435662884062257473692284509516<br>
90849603980134001723930671666823555245252804609722<br>
99503534226472524250874054075591789781264330331690<br>

ANS: 55913

SOLUTION: python

str = [int(i) for i in str.split("\n")]
print sum(str)

============================================================================================================================

QUESTION 5:
Starting from upper left box of a 2X2 table, and only being able to move to the right and down, there are exactly 6 routes to the bottom right box<br>
<img src='http://i.imgur.com/Q5l33XX.gif'>
<br>
Let the number of solutuons for a 15X15 table be N?
Find the first five digits of N.

!*ANS*! 26525

SOLUTION: Use the formula (2n)!/n!*n!

see this answer on SO http://stackoverflow.com/a/2200425

=============================================================================================================================