# Euler problems/171 to 180

(Difference between revisions)

## 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:

```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```

## 6 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]```

## 7 Problem 177

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`