Accumulative Effect

I have recently been watching re-runs of the 90's sitcom "Home Improvement" and I think the design of the Taylor's house is just perfect.  After some googling, I stumbled across this site, which among other things had a plan of the ground floor and (modified) basement of Tim the Tool-man's house.  I grabbed the downloads and posted them here (in case that site ever goes down).

I created here (hosted as a mirror to the original here and here).

The series, 1^(1) + 2^(2) + 3^(3) + ... + 10^(10) = 10405071317.

Find the last ten digits of the series, 1^(1) + 2^(2) + 3^(3) + ... + 1000^(1000).

My solution in Ruby:

sum = 0
for i in 1..1000 do
  sum += i**i
end
str = sum.to_s
 
puts str[str.length - 10,str.length]

s = 0
(1..1000).inject { |s, x| s + x ** x } % (10 ** 10)
str = s.to_s
puts str[str.length - 10,str.length]

Recently I had do to a lots of PostgreSQL database administration as I needed to move several databases onto  a production server.  PostgreSQL is one of the most robust, open source database servers available, and for my money, faster and generally better than MySQL. Like MySQL database server, it provides utilities for creating a backup.

Backup database using pg_dump command. pg_dump is a utility for backing up a PostgreSQL database. It dumps only one database at a time.

$ pg_dump table | gzip -c > table.dump.tar.gz

Another option is use to pg_dumpall command. As a name suggest it dumps (backs up) each database, and preserves cluster-wide data such as users and groups. You can use it as follows:

$ pg_dumpall | gzip -c > all.dump.tar.gz

The Fibonacci sequence is defined by the recurrence relation:

F_(n) = F_(n−1) + F_(n−2), where F_(1) = 1 and F_(2) = 1.

Hence the first 12 terms will be:

F_(1) = 1
F_(2) = 1
F_(3) = 2
F_(4) = 3
F_(5) = 5
F_(6) = 8
F_(7) = 13
F_(8) = 21
F_(9) = 34
F_(10) = 55
F_(11) = 89
F_(12) = 144

The 12th term, F_(12), is the first term to contain three digits.

What is the first term in the Fibonacci sequence to contain 1000 digits?

My solution in Ruby:

t1, t2, term = 1, 2, 3
loop do
  temp = t1 + t2
  t1 = t2
  t2 = temp
  term += 1
  temp_s = temp.to_s
  break if temp_s.length >= 1000
end
puts term

@@words = { 1 => "one",2 => "two",3 => "three",4 => "four",5 => "five",6 => "six",7 => "seven",8 => "eight",9 => "nine",10 => "ten",11 => "eleven",12 => "twelve",13 => "thirteen",14 => "fourteen",15 => "fifteen",16 => "sixteen",17 => "seventeen",18 => "eighteen",19 => "nineteen",20 => "twenty",30 => "thirty",40 => "forty",50 => "fifty",60 => "sixty",70 => "seventy",80 => "eighty",90 => "ninety",100 => "hundred",1000 => "thousand",0 => "" }
count = 0;
 
def one_to_ninetynine(base)
  icount = 0
  for i in 1..19 do
    icount += base + @@words[i].length
  end
  j = 10
  until j == 90
    j += 10
    icount += base + @@words[j].length
    for k in 1..9 do
      icount += base + @@words[j].length + @@words[k].length
    end
  end
  icount
end
 
count += one_to_ninetynine(0)
 
for l in 1..9 do
  count += @@words [l].length + (@@words[100].length)
  count += one_to_ninetynine(@@words[l].length + (@@words[100].length) + 3)
end
count += @@words[1].length + @@words[1000].length
 
puts count

2^(15) = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.

What is the sum of the digits of the number 2^(1000)?

My solution in Ruby:

sum, number = 0, 2**1000
str = number.to_s
y = str.scan(/./)
y.each do |c|
	sum += c.to_i
end
puts sum

Work out the first ten digits of the sum of the following one-hundred 50-digit numbers.
(numbers omitted)

My solution in Ruby:

 numbers = [
37107287533902102798797998220837590246510135740250,
46376937677490009712648124896970078050417018260538,
74324986199524741059474233309513058123726617309629,
91942213363574161572522430563301811072406154908250,
23067588207539346171171980310421047513778063246676,
89261670696623633820136378418383684178734361726757,
28112879812849979408065481931592621691275889832738,
44274228917432520321923589422876796487670272189318,
47451445736001306439091167216856844588711603153276,
70386486105843025439939619828917593665686757934951,
62176457141856560629502157223196586755079324193331,
64906352462741904929101432445813822663347944758178,
92575867718337217661963751590579239728245598838407,
58203565325359399008402633568948830189458628227828,
80181199384826282014278194139940567587151170094390,
35398664372827112653829987240784473053190104293586,
86515506006295864861532075273371959191420517255829,
71693888707715466499115593487603532921714970056938,
54370070576826684624621495650076471787294438377604,
53282654108756828443191190634694037855217779295145,
36123272525000296071075082563815656710885258350721,
45876576172410976447339110607218265236877223636045,
17423706905851860660448207621209813287860733969412,
81142660418086830619328460811191061556940512689692,
51934325451728388641918047049293215058642563049483,
62467221648435076201727918039944693004732956340691,
15732444386908125794514089057706229429197107928209,
55037687525678773091862540744969844508330393682126,
18336384825330154686196124348767681297534375946515,
80386287592878490201521685554828717201219257766954,
78182833757993103614740356856449095527097864797581,
16726320100436897842553539920931837441497806860984,
48403098129077791799088218795327364475675590848030,
87086987551392711854517078544161852424320693150332,
59959406895756536782107074926966537676326235447210,
69793950679652694742597709739166693763042633987085,
41052684708299085211399427365734116182760315001271,
65378607361501080857009149939512557028198746004375,
35829035317434717326932123578154982629742552737307,
94953759765105305946966067683156574377167401875275,
88902802571733229619176668713819931811048770190271,
25267680276078003013678680992525463401061632866526,
36270218540497705585629946580636237993140746255962,
24074486908231174977792365466257246923322810917141,
91430288197103288597806669760892938638285025333403,
34413065578016127815921815005561868836468420090470,
23053081172816430487623791969842487255036638784583,
11487696932154902810424020138335124462181441773470,
63783299490636259666498587618221225225512486764533,
67720186971698544312419572409913959008952310058822,
95548255300263520781532296796249481641953868218774,
76085327132285723110424803456124867697064507995236,
37774242535411291684276865538926205024910326572967,
23701913275725675285653248258265463092207058596522,
29798860272258331913126375147341994889534765745501,
18495701454879288984856827726077713721403798879715,
38298203783031473527721580348144513491373226651381,
34829543829199918180278916522431027392251122869539,
40957953066405232632538044100059654939159879593635,
29746152185502371307642255121183693803580388584903,
41698116222072977186158236678424689157993532961922,
62467957194401269043877107275048102390895523597457,
23189706772547915061505504953922979530901129967519,
86188088225875314529584099251203829009407770775672,
11306739708304724483816533873502340845647058077308,
82959174767140363198008187129011875491310547126581,
97623331044818386269515456334926366572897563400500,
42846280183517070527831839425882145521227251250327,
55121603546981200581762165212827652751691296897789,
32238195734329339946437501907836945765883352399886,
75506164965184775180738168837861091527357929701337,
62177842752192623401942399639168044983993173312731,
32924185707147349566916674687634660915035914677504,
99518671430235219628894890102423325116913619626622,
73267460800591547471830798392868535206946944540724,
76841822524674417161514036427982273348055556214818,
97142617910342598647204516893989422179826088076852,
87783646182799346313767754307809363333018982642090,
10848802521674670883215120185883543223812876952786,
71329612474782464538636993009049310363619763878039,
62184073572399794223406235393808339651327408011116,
66627891981488087797941876876144230030984490851411,
60661826293682836764744779239180335110989069790714,
85786944089552990653640447425576083659976645795096,
66024396409905389607120198219976047599490197230297,
64913982680032973156037120041377903785566085089252,
16730939319872750275468906903707539413042652315011,
94809377245048795150954100921645863754710598436791,
78639167021187492431995700641917969777599028300699,
15368713711936614952811305876380278410754449733078,
40789923115535562561142322423255033685442488917353,
44889911501440648020369068063960672322193204149535,
41503128880339536053299340368006977710650566631954,
81234880673210146739058568557934581403627822703280,
82616570773948327592232845941706525094512325230608,
22918802058777319719839450180888072429661980811197,
77158542502016545090413245809786882778948721859617,
72107838435069186155435662884062257473692284509516,
20849603980134001723930671666823555245252804609722,
53503534226472524250874054075591789781264330331690 ]
 
sum = 0
numbers.each do |i|
  sum += i
end
sum_s = sum.to_s
puts sum_s[0,10]

The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.

Find the sum of all the primes below two million.

My solution in Ruby:

def is_prime ( p )
  if p == 2
    return true
  elsif p <= 1 || p % 2 == 0
    return false
  else
    (3 .. Math.sqrt(p)).step(2) do |i|
      if p % i == 0
        return false
      end
    end
    return true
  end
end
 
sum = 0
for i in 2..2000000
  if is_prime(i)
    sum += i
  end
end
puts sum

Find the greatest product of five consecutive digits in the 1000-digit number.

73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450

My solution in Ruby:

var = %&
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450&
 
arr = var.split( // )
arr.delete "\n"
big = 0;
for i in 0..arr.length - 5
  next if Integer(arr[i]) == 0
  tmp = Integer(arr[i])
  1.upto(4) { |j| tmp = tmp * Integer(arr[i + j]) }
  big = tmp if tmp > big
end
puts big

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6^(th) prime is 13.

What is the 10001^(st) prime number?

My solution in Ruby:

def is_prime ( p )
  if p == 2
    return true
  elsif p <= 1 || p % 2 == 0
    return false
  else
    (3 .. Math.sqrt(p)).step(2) do |i|
      if p % i == 0
        return false
      end
    end
    return true
  end
end
 
prime_count = 6
prime_number = 13
number = 13
while prime_count < 10001 do
  number += 2
  if is_prime(number)
    prime_count += 1
    prime_number = number
  end
end
puts '***********'
puts "#{prime_count}: #{prime_number}"