# Difference between revisions of "Euler problems/171 to 180"

From HaskellWiki

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(add problem 175) |
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Solution: |
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<haskell> |
<haskell> |
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− | problem_175 = undefined |
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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> |
</haskell> |
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## Revision as of 13:40, 29 January 2008

## Contents

## 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
```