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Euler problems/181 to 190

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1 Problem 181

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. Daniel.is.fischer

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:

pmax x a=a*(log x-log a)
tofloat x=encodeFloat  x 0
fun x=
    div n1 $gcd n1 x
    where
    e=exp 1
    n=floor(fromInteger x/e)
    n1=snd.maximum$[(b,a)|a<-[n..n+1],let b=pmax (tofloat x) (tofloat a)]
n `splitWith` p = doSplitWith 0 n
	where doSplitWith s t
		| p `divides` t = doSplitWith (s+1) (t `div` p)
		| otherwise     = (s, t)
d `divides` n = n `mod` d == 0
funD x
    |is25 k=(-x)
    |otherwise =x
    where 
    k=fun x
is25 x
    |s==1=True
    |otherwise=False
    where
    s=snd(splitWith (snd (splitWith x 2)) 5)
problem_183 =sum[funD a|a<- [5..10000]]