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Euler problems/181 to 190

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main = print answer
 
main = print answer
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</haskell>
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== [http://projecteuler.net/index.php?section=problems&id=184 Problem 184] ==
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Triangles containing the origin.
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Solution:
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<haskell>
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problem_184 = undefined
 
</haskell>
 
</haskell>

Revision as of 00:09, 1 March 2008

Contents

1 Problem 181

Investigating in how many ways objects of two different colours can be grouped.

2 Problem 182

RSA encryption.

Solution:

fun a1 b1 = sum [ e | e <- [2..a*b-1],
                      gcd e (a*b) == 1,
                      gcd (e-1) a == 2,
                      gcd (e-1) b == 2 ]
  where a = a1-1
        b = b1-1
 
problem_182 = fun 1009 3643

3 Problem 183

Maximum product of parts.

Solution:

-- Does the decimal expansion of p/q terminate?
terminating p q = 1 == reduce [2,5] (q `div` gcd p q)
        where reduce   []   n = n
              reduce (x:xs) n | n `mod` x == 0 = reduce (x:xs) (n `div` x)
                              | otherwise      = reduce xs n
 
-- The expression (round $ fromIntegral n / e) computes the integer k
-- for which (n/k)^k is at a maximum. Also note that, given a rational number
-- r and a natural number k, the decimal expansion of r^k terminates if
-- and only if the decimal expansion of r does.
answer = sum [if terminating n (round $ fromIntegral n / e) then -n else n
                | n <- [5 .. 10^4]]
        where e = exp 1
 
main = print answer

4 Problem 184

Triangles containing the origin.

Solution:

problem_184 = undefined