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Euler problems/161 to 170

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(Added problem_164)
(Added solution for problem 166)
Line 47: Line 47:
 
Solution:
 
Solution:
 
<haskell>
 
<haskell>
problem_166 = undefined
+
problem_166 =
  +
sum [ product (map count [[0, c, b-d, a-b-d],
  +
[0, b-a, c+d-a, b+d-a],
  +
[0, -b-c, a-b-c-d, -c-d],
  +
[0, a, d, c+d]])|
  +
a <- [-9..9],
  +
b <- [-9+a..9+a],
  +
c <- [-9..9],
  +
d <- [-9+a-c..9+a-c]]
  +
where
  +
count xs
  +
|u<l=0
  +
|otherwise=u-l+1
  +
where
  +
l = -minimum xs
  +
u = 9-maximum xs
 
</haskell>
 
</haskell>
   
Line 56: Line 56:
 
<haskell>
 
<haskell>
 
problem_167 = undefined
 
problem_167 = undefined
  +
</haskell>
  +
  +
== [http://projecteuler.net/index.php?section=view&id=168 Problem 168] ==
  +
Number Rotations
  +
  +
Solution:
  +
<haskell>
  +
problem_168 = undefined
  +
</haskell>
  +
  +
== [http://projecteuler.net/index.php?section=view&id=169 Problem 169] ==
  +
Exploring the number of different ways a number can be expressed as a sum of powers of 2.
  +
  +
Solution:
  +
<haskell>
  +
problem_169 = undefined
  +
</haskell>
  +
  +
== [http://projecteuler.net/index.php?section=view&id=170 Problem 170] ==
  +
Find the largest 0 to 9 pandigital that can be formed by concatenating products.
  +
  +
Solution:
  +
<haskell>
  +
problem_170 = undefined
 
</haskell>
 
</haskell>

Revision as of 05:30, 21 January 2008

Contents

1 Problem 161

Triominoes

Solution:

problem_161 = undefined

2 Problem 162

Hexadecimal numbers

Solution:

problem_162 = undefined

3 Problem 163

Cross-hatched triangles

Solution:

problem_163 = undefined

4 Problem 164

Numbers for which no three consecutive digits have a sum greater than a given value.

Solution:

addDigit x = [[sum [x !! b !! c | c <- [0..9-a-b]] | b <- [0..9-a]] | a<-[0..9]]
x3 = [[10-a-b | b <- [0..9-a]] | a <- [0..9]]
x20 = iterate addDigit x3 !! 17
problem_164 = sum [x20 !! a !! b | a <- [1..9], b <- [0..9-a]]

5 Problem 165

Intersections

Solution:

problem_165 = undefined

6 Problem 166

Criss Cross

Solution:

problem_166 = 
    sum [ product (map count [[0, c, b-d, a-b-d], 
            [0, b-a, c+d-a, b+d-a], 
            [0, -b-c, a-b-c-d, -c-d],
            [0, a, d, c+d]])|
        a <- [-9..9], 
        b <- [-9+a..9+a],
        c <- [-9..9],
        d <- [-9+a-c..9+a-c]]
    where
    count xs 
        |u<l=0 
        |otherwise=u-l+1
        where
        l = -minimum xs 
        u = 9-maximum xs

7 Problem 167

Investigating Ulam sequences

Solution:

problem_167 = undefined

8 Problem 168

Number Rotations

Solution:

problem_168 = undefined

9 Problem 169

Exploring the number of different ways a number can be expressed as a sum of powers of 2.

Solution:

problem_169 = undefined

10 Problem 170

Find the largest 0 to 9 pandigital that can be formed by concatenating products.

Solution:

problem_170 = undefined