Tag Archives: Big Int

Project Euler: Problem 25

November 6, 2009 Torleif 9 Comments

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:

$F_1 = 1 \\ F_2 = 1 \\ \ldots \\ F_{11} = 89 \\ F_{12} = 144$

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?

Continue reading Project Euler: Problem 25 →

Project Euler, Software Development

Project Euler: Problem 16

November 5, 2009 Torleif Leave a comment

$2^{15} = 32768$ and the sum of its digits is
$3 + 2 + 7 + 6 + 8 = 26$ .

What is the sum of the digits of the number $2^{1000}$ ?

Continue reading Project Euler: Problem 16 →

Project Euler, Software Development

Project Euler: Problem 13

October 4, 2009 Torleif 3 Comments

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

37107287533902102798797998220837590246510135740250
46376937677490009712648124896970078050417018260538
74324986199524741059474233309513058123726617309629
91942213363574161572522430563301811072406154908250
23067588207539346171171980310421047513778063246676
89261670696623633820136378418383684178734361726757
28112879812849979408065481931592621691275889832738
44274228917432520321923589422876796487670272189318 Continue reading Project Euler: Problem 13 →

Project Euler, Software Development

Project Euler: Problem 8

September 24, 2009 Torleif 5 Comments

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