Count consecutive summers def count_consecutive_summers(n): Like a majestic wild horse waiting for the rugged hero to tame it, positive integers can be broken down as sums of consecutive positive integers in various ways. For example, the integer 42 often used as placeholder in this kind of discussions can be broken down into such a sum in four different ways: (a) 3 + 4 + 5 + 6 + 7 + 8 + 9, (b) 9 + 10 + 11 + 12, (c) 13 + 14 + 15 and (d) 42. As the last solution (d) shows, any positive integer can always be trivially expressed as a singleton sum that consists of that integer alone. Given a positive integer n, determine how many different ways it can be expressed as a sum of consecutive positive integers, and return that count. The number of ways that a positive integer n can be represented as a sum of consecutive integers is called its politeness, and can also be computed by tallying up the number of odd divisors of that number. However, note that the linked Wikipedia de0inition includes only nontrivial sums that consist of at least two components, so according to that de0inition, the politeness of 42 would be 3, not 4, due to its odd divisors being 3, 7 and 21. n Expected result 42 4 99 6 92 2 Powers of two are therefore the least polite of all numbers. Perhaps these powers being the fundamental building blocks of all numbers in binary representation also made them believe their own hype and balloon up to be too big for their britches. (Fame tends to do that even to the most level-headed of us.) As an exercise in combinatorics, how would you concisely characterize the opposite extreme of “most polite” numbers that can be represented as sums of consecutive integers in more ways than any number less than them?
Count consecutive summers
def count_consecutive_summers(n):Like a majestic wild horse waiting for the rugged hero to tame it, positive integers can be broken down as sums of consecutive positive integers in various ways. For example, the integer 42 often used as placeholder in this kind of discussions can be broken down into such a sum in four different ways: (a) 3 + 4 + 5 + 6 + 7 + 8 + 9, (b) 9 + 10 + 11 + 12, (c) 13 + 14 + 15 and (d) 42. As the last solution (d) shows, any positive integer can always be trivially expressed as a singleton sum that consists of that integer alone. Given a positive integer n, determine how many different ways it can be expressed as a sum of consecutive positive integers, and return that count.
The number of ways that a positive integer n can be represented as a sum of consecutive integers is called its politeness, and can also be computed by tallying up the number of odd divisors of that number. However, note that the linked Wikipedia de0inition includes only nontrivial sums that consist of at least two components, so according to that de0inition, the politeness of 42 would be 3, not 4, due to its odd divisors being 3, 7 and 21.
|
n |
Expected result |
|
42 |
4 |
|
99 |
6 |
|
92 |
2 |
Powers of two are therefore the least polite of all numbers. Perhaps these powers being the fundamental building blocks of all numbers in binary representation also made them believe their own hype and balloon up to be too big for their britches. (Fame tends to do that even to the most level-headed of us.) As an exercise in combinatorics, how would you concisely characterize the opposite extreme of “most polite” numbers that can be represented as sums of consecutive integers in more ways than any number less than them?
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