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"content": "As behooves any intelligent schoolboy, Kevin Sun is studying psycowlogy, cowculus, and cryptcowgraphy at the Bovinia State University (BGU) under Farmer Ivan. During his Mathematics of Olympiads (MoO) class, Kevin was confronted with a weird functional equation and needs your h... |
[
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"content": "Background\nThe sequence in the title is A245788 \"n times the number of 1's in the binary expansion of n\" (\"times\" here means multiplication), which starts like this:\n1, 2, 6, 4, 10, 12, 21, 8, 18, 20,\n33, 24, 39, 42, 60, 16, 34, 36, 57, 40,\n63, 6... |
[
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"role": "user",
"content": "Cosider a sequence, consisting of n integers: a1, a2, ..., an. Jeff can perform the following operation on sequence a:\n\n * take three integers v, t, k (1 ≤ v, t ≤ n; 0 ≤ k; v + tk ≤ n), such that av = av + t, av + t = av + 2t, ..., av + t(k - 1) = av + tk; \n * remove eleme... |
[
{
"role": "user",
"content": "Some built-in functions in PHP return mixed types, like file_get_contents that returns both string or false. Union structs in C can be used to simulate this, but is there a way to make it polyglot, that is, can be run in both PHP and C without (major) modification? Macros is of... |
[{"role":"user","content":"A ski base is planned to be built in Walrusland. Recently, however, the p(...TRUNCATED) |
[{"role":"user","content":"Input\nA string S of length between 10 and 16 inclusive. The characters a(...TRUNCATED) |
[{"role":"user","content":"The question: Given an a number n ≥ 2, how many distinct pairs of point(...TRUNCATED) |
[{"role":"user","content":"A sequence of non-negative integers a_1, a_2, ..., a_n is called growing (...TRUNCATED) |
[{"role":"user","content":"In this challenge, you must design a species of single-celled organisms t(...TRUNCATED) |
[{"role":"user","content":"The small nation of Erratica prides itself on defying conventions establi(...TRUNCATED) |
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