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Euler problems/171 to 180

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< Euler problems
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Contents

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

Integer angled Quadrilaterals.

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