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Euler problems/171 to 180

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Do them on your own!
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== [http://projecteuler.net/index.php?section=problems&id=171 Problem 171] ==
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Finding numbers for which the sum of the squares of the digits is a square.
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Solution:
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<haskell>
  +
problem_171 = undefined
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</haskell>
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== [http://projecteuler.net/index.php?section=problems&id=172 Problem 172] ==
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Investigating numbers with few repeated digits.
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Solution:
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<haskell>
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problem_172 = undefined
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</haskell>
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== [http://projecteuler.net/index.php?section=problems&id=173 Problem 173] ==
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Using up to one million tiles how many different "hollow" square laminae can be formed?
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Solution:
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<haskell>
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problem_173=
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let c=div (10^6) 4
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xm=floor$sqrt $fromIntegral c
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k=[div c x|x<-[1..xm]]
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in sum k-(div (xm*(xm+1)) 2)
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</haskell>
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== [http://projecteuler.net/index.php?section=problems&id=174 Problem 174] ==
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Counting the number of "hollow" square laminae that can form one, two, three, ... distinct arrangements.
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Solution:
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<haskell>
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problem_174 = undefined
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</haskell>
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== [http://projecteuler.net/index.php?section=problems&id=175 Problem 175] ==
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Fractions involving the number of different ways a number can be expressed as a sum of powers of 2.
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Solution:
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<haskell>
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sternTree x 0=[]
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sternTree x y=
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m:sternTree y n
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where
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(m,n)=divMod x y
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findRat x y
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|odd l=take (l-1) k++[last k-1,1]
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|otherwise=k
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where
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k=sternTree x y
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l=length k
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p175 x y=
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init$foldl (++) "" [a++","|
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a<-map show $reverse $filter (/=0)$findRat x y]
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problems_175=p175 123456789 987654321
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test=p175 13 17
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</haskell>
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== [http://projecteuler.net/index.php?section=problems&id=176 Problem 176] ==
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Rectangular triangles that share a cathetus.
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Solution:
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<haskell>
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problem_176 = undefined
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</haskell>
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== [http://projecteuler.net/index.php?section=problems&id=177 Problem 177] ==
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Integer angled Quadrilaterals.
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Solution:
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<haskell>
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problem_177 = undefined
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</haskell>
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== [http://projecteuler.net/index.php?section=problems&id=178 Problem 178] ==
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Step Numbers
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Solution:
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<haskell>
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problem_178 = undefined
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</haskell>
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== [http://projecteuler.net/index.php?section=problems&id=179 Problem 179] ==
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Consecutive positive divisors.
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Solution:
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<haskell>
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problem_179 = undefined
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</haskell>
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== [http://projecteuler.net/index.php?section=problems&id=180 Problem 180] ==
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  +
Solution:
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<haskell>
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problem_180 = undefined
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</haskell>

Revision as of 06:24, 30 January 2008

Contents

1 Problem 171

Finding numbers for which the sum of the squares of the digits is a square.

Solution:

problem_171 = undefined

2 Problem 172

Investigating numbers with few repeated digits.

Solution:

problem_172 = undefined

3 Problem 173

Using up to one million tiles how many different "hollow" square laminae can be formed? Solution:

problem_173=
    let c=div (10^6) 4
        xm=floor$sqrt $fromIntegral c
        k=[div c x|x<-[1..xm]]
    in  sum k-(div (xm*(xm+1)) 2)

4 Problem 174

Counting the number of "hollow" square laminae that can form one, two, three, ... distinct arrangements.

Solution:

problem_174 = undefined

5 Problem 175

Fractions involving the number of different ways a number can be expressed as a sum of powers of 2. Solution:

sternTree x 0=[]
sternTree x y=
    m:sternTree y n  
    where
    (m,n)=divMod x y
findRat x y
    |odd l=take (l-1) k++[last k-1,1]
    |otherwise=k
    where
    k=sternTree x y
    l=length k
p175 x y= 
    init$foldl (++) "" [a++","|
    a<-map show $reverse $filter (/=0)$findRat x y]
problems_175=p175 123456789 987654321
test=p175 13 17

6 Problem 176

Rectangular triangles that share a cathetus. Solution:

problem_176 = undefined

7 Problem 177

Integer angled Quadrilaterals.

Solution:

problem_177 = undefined

8 Problem 178

Step Numbers Solution:

problem_178 = undefined

9 Problem 179

Consecutive positive divisors. Solution:

problem_179 = undefined

10 Problem 180

Solution:

problem_180 = undefined