# Euler problems/171 to 180

From HaskellWiki

## 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:

```
factorial n = product [1..toInteger n]
fallingFactorial x n = product [x - fromInteger i | i <- [0..toInteger n - 1] ]
choose n k = fallingFactorial n k `div` factorial k
-- how many numbers can we get having d digits and p positions
p172 0 _ = 0
p172 d p
| p < 4 = d^p
| otherwise =
(p172' p) + p*(p172' (p-1)) + (choose p 2)*(p172' (p-2)) + (choose p 3)*(p172' (p-3))
where
p172' = p172 (d-1)
problem_172= (p172 10 18) * 9 `div` 10
```

## 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:

```
--k=47547
--2*k+1=95095 = 5*7*11*13*19
lst=[5,7,11,13,19]
primes=[2,3,5,7,11]
problem_176 =
product[a^b|(a,b)<-zip primes (reverse n)]
where
la=div (last lst+1) 2
m=map (\x->div x 2)$init lst
n=m++[la]
```

## 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
```