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

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:

```--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

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
```