# Difference between revisions of "Euler problems/181 to 190"

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-- The expression (round $ fromIntegral n / e) computes the integer k |
-- The expression (round $ fromIntegral n / e) computes the integer k |
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− | -- for which (n/k)^k is at a maximum. |
+ | -- 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 |
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+ | -- and only if the decimal expansion of r does. |
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answer = sum [if terminating n (round $ fromIntegral n / e) then -n else n |
answer = sum [if terminating n (round $ fromIntegral n / e) then -n else n |
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| n <- [5 .. 10^4]] |
| n <- [5 .. 10^4]] |

## Revision as of 20:30, 24 February 2008

## 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

## 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
```

## 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
```