# Euler problems/171 to 180

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< Euler problems(Difference between revisions)

(add problem 173) |
(add problem 175) |

## Revision as of 13:40, 29 January 2008

## 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:

problem_176 = undefined

## 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