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Euler problems/171 to 180

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== [http://projecteuler.net/index.php?section=problems&id=161 Problem 161] ==
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== [http://projecteuler.net/index.php?section=problems&id=171 Problem 171] ==
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Triominoes
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Finding numbers for which the sum of the squares of the digits is a square.
Solution:
Solution:
<haskell>
<haskell>
-
problem_161 = undefined
+
problem_171 = undefined
</haskell>
</haskell>
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== [http://projecteuler.net/index.php?section=problems&id=162 Problem 162] ==
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== [http://projecteuler.net/index.php?section=problems&id=172 Problem 172] ==
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Hexadecimal numbers
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Investigating numbers with few repeated digits.
Solution:
Solution:
<haskell>
<haskell>
-
problem_162 = undefined
+
problem_172 = undefined
</haskell>
</haskell>
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== [http://projecteuler.net/index.php?section=problems&id=163 Problem 163] ==
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== [http://projecteuler.net/index.php?section=problems&id=173 Problem 173] ==
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Cross-hatched triangles
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Using up to one million tiles how many different "hollow" square laminae can be formed?
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Solution:
Solution:
<haskell>
<haskell>
-
problem_163 = undefined
+
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)
</haskell>
</haskell>
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== [http://projecteuler.net/index.php?section=problems&id=164 Problem 164] ==
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== [http://projecteuler.net/index.php?section=problems&id=174 Problem 174] ==
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Numbers for which no three consecutive digits have a sum greater than a given value.
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Counting the number of "hollow" square laminae that can form one, two, three, ... distinct arrangements.
Solution:
Solution:
<haskell>
<haskell>
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addDigit x = [[sum [x !! b !! c | c <- [0..9-a-b]] | b <- [0..9-a]] | a<-[0..9]]
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problem_174 = undefined
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x3 = [[10-a-b | b <- [0..9-a]] | a <- [0..9]]
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x20 = iterate addDigit x3 !! 17
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problem_164 = sum [x20 !! a !! b | a <- [1..9], b <- [0..9-a]]
+
</haskell>
</haskell>
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== [http://projecteuler.net/index.php?section=problems&id=165 Problem 165] ==
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== [http://projecteuler.net/index.php?section=problems&id=175 Problem 175] ==
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Intersections
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Fractions involving the number of different ways a number can be expressed as a sum of powers of 2.
-
 
+
Solution:
Solution:
<haskell>
<haskell>
-
problem_165 = undefined
+
problem_175 = undefined
</haskell>
</haskell>
-
== [http://projecteuler.net/index.php?section=problems&id=166 Problem 166] ==
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== [http://projecteuler.net/index.php?section=problems&id=176 Problem 176] ==
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Criss Cross
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Rectangular triangles that share a cathetus.
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+
Solution:
Solution:
<haskell>
<haskell>
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problem_166 =
+
problem_176 = undefined
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sum [ product (map count [[0, c, b-d, a-b-d],
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[0, b-a, c+d-a, b+d-a],
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[0, -b-c, a-b-c-d, -c-d],
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[0, a, d, c+d]])|
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a <- [-9..9],
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b <- [-9+a..9+a],
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c <- [-9..9],
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d <- [-9+a-c..9+a-c]]
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where
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count xs
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|u<l=0
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|otherwise=u-l+1
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where
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l = -minimum xs
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u = 9-maximum xs
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</haskell>
</haskell>
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== [http://projecteuler.net/index.php?section=problems&id=167 Problem 167] ==
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== [http://projecteuler.net/index.php?section=problems&id=177 Problem 177] ==
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Investigating Ulam sequences
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Integer angled Quadrilaterals.
Solution:
Solution:
<haskell>
<haskell>
-
problem_167 = undefined
+
problem_177 = undefined
</haskell>
</haskell>
-
== [http://projecteuler.net/index.php?section=problems&id=168 Problem 168] ==
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== [http://projecteuler.net/index.php?section=problems&id=178 Problem 178] ==
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Number Rotations
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Step Numbers
-
 
+
Solution:
Solution:
<haskell>
<haskell>
-
problem_168 = undefined
+
problem_178 = undefined
</haskell>
</haskell>
-
== [http://projecteuler.net/index.php?section=problems&id=169 Problem 169] ==
+
== [http://projecteuler.net/index.php?section=problems&id=179 Problem 179] ==
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Exploring the number of different ways a number can be expressed as a sum of powers of 2.
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Consecutive positive divisors.
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+
Solution:
Solution:
<haskell>
<haskell>
-
problem_169 = undefined
+
problem_179 = undefined
</haskell>
</haskell>
-
== [http://projecteuler.net/index.php?section=problems&id=170 Problem 170] ==
+
== [http://projecteuler.net/index.php?section=problems&id=180 Problem 180] ==
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Find the largest 0 to 9 pandigital that can be formed by concatenating products.
+
Solution:
Solution:
<haskell>
<haskell>
-
problem_170 = undefined
+
problem_180 = undefined
</haskell>
</haskell>

Revision as of 13:27, 28 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: 

problem_175 = undefined

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
Retrieved from "http://www.haskell.org/haskellwiki/Euler_problems/171_to_180"