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Euler problems/181 to 190

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Investigating in how many ways objects of two different colours can be grouped.
 
Investigating in how many ways objects of two different colours can be grouped.
   
Solution: This was my code, published here without my permission nor any attribution, shame on whoever put it here. [[User:Daniel.is.fischer|Daniel.is.fischer]]
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{{sect-stub}}
   
 
== [http://projecteuler.net/index.php?section=problems&id=182 Problem 182] ==
 
== [http://projecteuler.net/index.php?section=problems&id=182 Problem 182] ==
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Solution:
 
Solution:
 
<haskell>
 
<haskell>
fun a1 b1 =
+
fun a1 b1 = sum [ e | e <- [2..a*b-1],
sum [ e |
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gcd e (a*b) == 1,
e <- [2..a*b-1],
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gcd (e-1) a == 2,
gcd e (a*b) == 1,
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gcd (e-1) b == 2 ]
gcd (e-1) a == 2,
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where a = a1-1
gcd (e-1) b == 2
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b = b1-1
]
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where
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problem_182 = fun 1009 3643
a=a1-1
 
b=b1-1
 
problem_182=fun 1009 3643
 
 
</haskell>
 
</haskell>
   

Revision as of 22:24, 24 February 2008

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