# Difference between revisions of "Euler problems/161 to 170"

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− | Do them on your own! |
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+ | == [http://projecteuler.net/index.php?section=problems&id=161 Problem 161] == |
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+ | Triominoes |
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+ | |||

+ | Solution: |
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+ | <haskell> |
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+ | problem_161 = undefined |
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+ | </haskell> |
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+ | |||

+ | == [http://projecteuler.net/index.php?section=problems&id=162 Problem 162] == |
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+ | Hexadecimal numbers |
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+ | |||

+ | Solution: |
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+ | <haskell> |
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+ | problem_162 = undefined |
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+ | </haskell> |
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+ | |||

+ | == [http://projecteuler.net/index.php?section=problems&id=163 Problem 163] == |
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+ | Cross-hatched triangles |
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+ | |||

+ | Solution: |
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+ | <haskell> |
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+ | problem_163 = undefined |
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+ | </haskell> |
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+ | |||

+ | == [http://projecteuler.net/index.php?section=problems&id=164 Problem 164] == |
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+ | Numbers for which no three consecutive digits have a sum greater than a given value. |
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+ | |||

+ | Solution: |
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+ | <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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+ | 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]] |
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+ | </haskell> |
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+ | |||

+ | == [http://projecteuler.net/index.php?section=problems&id=165 Problem 165] == |
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+ | Intersections |
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+ | |||

+ | Solution: |
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+ | <haskell> |
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+ | problem_165 = undefined |
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+ | </haskell> |
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+ | |||

+ | == [http://projecteuler.net/index.php?section=problems&id=166 Problem 166] == |
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+ | Criss Cross |
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+ | |||

+ | Solution: |
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+ | <haskell> |
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+ | problem_166 = |
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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> |
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+ | |||

+ | == [http://projecteuler.net/index.php?section=problems&id=167 Problem 167] == |
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+ | Investigating Ulam sequences |
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+ | |||

+ | Solution: |
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+ | <haskell> |
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+ | problem_167 = undefined |
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+ | </haskell> |
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+ | |||

+ | == [http://projecteuler.net/index.php?section=problems&id=168 Problem 168] == |
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+ | Number Rotations |
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+ | |||

+ | Solution: |
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+ | <haskell> |
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+ | problem_168 = undefined |
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+ | </haskell> |
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+ | |||

+ | == [http://projecteuler.net/index.php?section=problems&id=169 Problem 169] == |
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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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+ | |||

+ | Solution: |
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+ | <haskell> |
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+ | problem_169 = undefined |
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+ | </haskell> |
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+ | |||

+ | == [http://projecteuler.net/index.php?section=problems&id=170 Problem 170] == |
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+ | Find the largest 0 to 9 pandigital that can be formed by concatenating products. |
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+ | |||

+ | Solution: |
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+ | <haskell> |
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+ | problem_170 = undefined |
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+ | </haskell> |

## Revision as of 04:59, 30 January 2008

## Contents

## Problem 161

Triominoes

Solution:

```
problem_161 = undefined
```

## Problem 162

Hexadecimal numbers

Solution:

```
problem_162 = undefined
```

## Problem 163

Cross-hatched triangles

Solution:

```
problem_163 = undefined
```

## 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]]
```

## Problem 165

Intersections

Solution:

```
problem_165 = undefined
```

## 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
```

## Problem 167

Investigating Ulam sequences

Solution:

```
problem_167 = undefined
```

## Problem 168

Number Rotations

Solution:

```
problem_168 = undefined
```

## Problem 169

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

Solution:

```
problem_169 = undefined
```

## Problem 170

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

Solution:

```
problem_170 = undefined
```