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