Post tagged: programming puzzles

008 - paths across grid

See Problem 8: Find the greatest product of five consecutive digits in a 1000-digit number.

This is fairly straightforward. First we define the number, using Python's implicit string continuation:

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

Counting bouncy numbers

See Project Euler Problem 112: Find the point at which the porportion of bouncy numbers is 99%.

This is a simple problem to state, but has some tricks. First in the conversion of a number into its component digits. This can be neatly done with the [int (x) for x …

007 - 10001st prime

See Problem 7: What is the 10001st prime number?

This solution is fairly simple (and largely stolen from Aaron Gallagher):

def iter_primes ():
   # handle trivial case
   yield 2
   val = 1
   primesq_pairs = []
   while True:
      curr = None
      while (curr is None):
      val += 2
      curr = val
      for prime, square in primesq_pairs:
         if (curr < square …

Euler 035 - counting circular primes

See Problem 20.

Again, this rescues a lot of code from previous problems, but the solution is less than perfect. The Euler guidelines say that every problem should be computable within a minute, but despite much tweaking, this solution takes significantly longer.

For speed, primes should be generated only once …

Euler in Groovy 1: sum of numbers

The problem is:

Print the sum of numbers less than 1000 that are divisble by 5 or 3.

Already, we're exposed to a few nifty features of Groovy - ranges, and the functional methods on arrays like findAll:

// print the sum of numbers less than 1000 that are divisble by 5 …

Euler in Groovy 7: finding primes

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13. What is the 10001st prime number?

It seems a bit cumbersome, but use a sieve of erasthonenes to generate primes until we have collected the 10001st. Basically …