问题2595.礼貌的数字。礼貌。

Created byJan Orwat

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解决方案Stats

420 Solutions
130 Solvers

Last解决方案submitted on May 12, 2022

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丹尼尔·佩雷拉（Daniel Pereira）on 27 Jan 2016

There are some flaws when checking the solutions:

I think 15 has 4 combinations of sum of consecutive INTEGERS (as stated in the problem):
15 = 7+8 = 4+5+6 = 1+2+3+3+4+5 = 0+1+2+2+3+4+5;％0是整数。

或1025（您说5，我说9）：
1025 = 1022+1023 = sum(203:207) = sum(98:107) = sum(29:53) = sum(5:45) = sum(-4:45) = sum(-28:53) = sum(-97:107) = sum(-202:207); % negative numbers are integers too.

Jan Orwat2016年1月28日

I can see the flaw in the description now, I've missed repeating "positive", Thanks. Btw considering your interpretation 15 has 7 combinations: sum(-14:15),sum(-6:8),sum(-3:6),sum(0:5),sum(1:5),sum(4:6),sum(7:8). In this way 1025 should have 11 and conversion between our interpretations is "yours=2*mine+1"; to any of mine solutions of the form m:n, you can add "-m+1:n", the last thing is to add "-input+1:input"

John D'Errico2016年8月21日

An interesting problem, enough so that I chose to solve it in three essentially different ways. As always, there are various ways to solve any problem. The first two ways were essentially constructive, so counting the set of solutions for any N. The last used a formulaic approach.

Rafael S.T. Vieiraon 11 Aug 2020

Politeness is an integer sequence defined at https://oeis.org/A069283.

goc32021年1月13日

@Dyuman Joshi: I do not know why that error occurs. I do know that it essentially means that the user needs to wait and re-submit their solution at a later time, sometimes the next day.

By the way, it's best to not post solutions (or solution attempts) in comments. Questions or comments specific to a solution can be posted in a comment tied to said solution or solution attempt.