These problems are inspired in some of the problems from Project Euler. You can find them at https://projecteuler.net.

- The sum of the squares of the first 10 natural numbers is
1
^{2}+2^{2}+…+10^{2}=385. The square of the sum of the first 10 natural numbers is (1+2+…+10)^{2}=55^{2}=3025. Therefore, the difference between the sum of the squares of the first 10 natural numbers and the square of the sum of the first 10 natural numbers is 3025 − 385 = 2640.Write a function

*diffSqrs :: Integer -> Integer*that, given a natural*n*, returns the difference between the sum of the squares of the first*n*natural numbers and the square of the sum of the first*n*natural numbers. - A Pythagorean triplet are three natural numbers (
*a*,*b*,*c*) such that*a*^{2}+*b*^{2}=*c*^{2}. Write a function*pythagoreanTriplets :: Int -> [(Int, Int, Int)]*that, given a natural*n*≥1, returns the list of all Pythagorean tripletes that add up to*n*. Each triplet must be sorted in such a way that*a*≤*b*≤*c*and the list must be sorted according to*a*. - Write a function
*tartaglia :: [[Integer]]*that returns an infinite list with the rowss of the Tartaglia’s triangle (also known as Pascal’s triangle). - Write a function
*sumDigits :: Integer -> Integer*that returns the sum of all digits of a natural number. Use high order functions rather than recursion. - Write a function
*digitalRoot :: Integer -> Integer*that returns the digital root of a natural number. Use high order functions rather than recursion.

**Scoring**

Each function scores 20 points.

Public test cases

**Input**

diffSqrs 10 map pythagoreanTriplets [3,12,84] take 5 tartaglia sumDigits 32768 digitalRoot 65536

**Output**

2640 [[],[(3,4,5)],[(12,35,37),(21,28,35)]] [[1],[1,1],[1,2,1],[1,3,3,1],[1,4,6,4,1]] 26 7

Information

- Author
- Jordi Petit
- Language
- English
- Translator
- Jordi Petit
- Original language
- Catalan
- Other languages
- Catalan
- Official solutions
- Haskell
- User solutions
- Haskell