# Euler problems/31 to 40

### From HaskellWiki

(fix typo) |
(→[http://projecteuler.net/index.php?section=problems&id=31 Problem 31]: naive doubly recursive solution) |
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Line 3: | Line 3: | ||

Solution: | Solution: | ||

+ | |||

+ | This is the naive doubly recursive solution. Speed would be greatly improved by use of memoization, dynamic programming, or the closed form. | ||

<haskell> | <haskell> | ||

− | problem_31 = | + | problem_31 = pence 200 [1,2,5,10,20,50,100,200] |

+ | where pence 0 _ = 1 | ||

+ | pence n [] = 0 | ||

+ | pence n denominations@(d:ds) | ||

+ | | n < d = 0 | ||

+ | | otherwise = pence (n - d) denominations | ||

+ | + pence n ds | ||

</haskell> | </haskell> | ||

## Revision as of 14:22, 28 March 2007

## Contents |

## 1 Problem 31

Investigating combinations of English currency denominations.

Solution:

This is the naive doubly recursive solution. Speed would be greatly improved by use of memoization, dynamic programming, or the closed form.

problem_31 = pence 200 [1,2,5,10,20,50,100,200] where pence 0 _ = 1 pence n [] = 0 pence n denominations@(d:ds) | n < d = 0 | otherwise = pence (n - d) denominations + pence n ds

## 2 Problem 32

Find the sum of all numbers that can be written as pandigital products.

Solution:

problem_32 = undefined

## 3 Problem 33

Discover all the fractions with an unorthodox cancelling method.

Solution:

problem_33 = undefined

## 4 Problem 34

Find the sum of all numbers which are equal to the sum of the factorial of their digits.

Solution:

problem_34 = undefined

## 5 Problem 35

How many circular primes are there below one million?

Solution:

problem_35 = undefined

## 6 Problem 36

Find the sum of all numbers less than one million, which are palindromic in base 10 and base 2.

Solution:

problem_36 = undefined

## 7 Problem 37

Find the sum of all eleven primes that are both truncatable from left to right and right to left.

Solution:

problem_37 = undefined

## 8 Problem 38

What is the largest 1 to 9 pandigital that can be formed by multiplying a fixed number by 1, 2, 3, ... ?

Solution:

problem_38 = undefined

## 9 Problem 39

If p is the perimeter of a right angle triangle, {a, b, c}, which value, for p ≤ 1000, has the most solutions?

Solution:

problem_39 = undefined

## 10 Problem 40

Finding the nth digit of the fractional part of the irrational number.

Solution:

problem_40 = undefined