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]
UPDATE
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
Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:
21 22 23 24 25 20 7 8 9 10 19 6 1 2 11 18 5 4 3 12 17 16 15 14 13It can be verified that the sum of the numbers on the diagonals is 101.
What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?
My solution in Ruby:
corners = [1]
num = 1
add = 2
500.times do
4.times do
num += add
corners << num
end
add += 2
end
sum = 0
corners.each { |c| sum += c }
puts sum
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) = 144The 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
n! means n x (n – 1) x … x 3 x 2 x 1
Find the sum of the digits in the number 100!
My solution in Ruby:
sum = 0
factorial = 1
for i in 1..100
factorial = factorial * i
end
str = factorial.to_s
y = str.scan(/./)
y.each do |c|
sum += c.to_i
end
puts sum
If the numbers 1 to 5 are written out in words: one, two, three, four, five, then there are 3 + 3 + 5 + 4 + 4 = 19 letters used in total.
If all the numbers from 1 to 1000 (one thousand) inclusive were written out in words, how many letters would be used?
NOTE: Do not count spaces or hyphens. For example, 342 (three hundred and forty-two) contains 23 letters and 115 (one hundred and fifteen) contains 20 letters. The use of “and” when writing out numbers is in compliance with British usage.
My solution in Ruby:
@@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
The following iterative sequence is defined for the set of positive integers:
n -> n/2 (n is even)
n -> 3n + 1 (n is odd)Using the rule above and starting with 13, we generate the following sequence:
13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1
It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.Which starting number, under one million, produces the longest chain?
NOTE: Once the chain starts the terms are allowed to go above one million.
My solution in Ruby:
highchain = {}
high = 0
1000000.downto(1) do |i|
links = 0
result = i
loop do
links += 1
if result.odd?
result = (result * 3) + 1
else
result = result / 2
end
break if result == 1
end
highchain = {i, links} if links > high
high = links if links > high
end
highchain.each { |k,v| puts "#{k} has the longest chain of #{v} links!"}
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]