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Omni-MATH / Given n countries with three representatives each, m committees A(1),A(2),…,A(m) are called a cycle if [i](i)[/i] each committee has n members, one from each country; [i](ii)[/i] n…

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problem

Given n n countries with three representatives each, m m committees A(1),A(2),…,A(m) A(1),A(2), \ldots, A(m) are called a cycle if [i](i)[/i] each committee has n n members, one from each country; [i](ii)[/i] no two committees have the same membership; [i](iii)[/i] for $ i \equal{} 1, 2, \ldots,m$, committee A(i) A(i) and committee $ A(i \plus{} 1)$ have no member in common, where $ A(m \plus{} 1)$ denotes A(1); A(1); [i](iv)[/i] if $ 1 < |i \minus{} j| < m \minus{} 1,$ then committees A(i) A(i) and A(j) A(j) have at least one member in common. Is it possible to have a cycle of 1990 committees with 11 countries?
Plain-text mathematical notation (without MathML)
Given n countries with three representatives each, m committees A(1),A(2),…,A(m) are called a cycle if

[i](i)[/i] each committee has n members, one from each country;
[i](ii)[/i] no two committees have the same membership;
[i](iii)[/i] for $ i \equal{} 1, 2, \ldots,m$, committee A(i) and committee $ A(i \plus{} 1)$ have no member in common, where $ A(m \plus{} 1)$ denotes A(1);
[i](iv)[/i] if $ 1 < |i \minus{} j| < m \minus{} 1,$ then committees A(i) and A(j) have at least one member in common.

Is it possible to have a cycle of 1990 committees with 11 countries?
Original LaTeX notation
Given $ n$ countries with three representatives each, $ m$ committees $ A(1),A(2), \ldots, A(m)$ are called a cycle if

[i](i)[/i] each committee has $ n$ members, one from each country;
[i](ii)[/i] no two committees have the same membership;
[i](iii)[/i] for $ i \equal{} 1, 2, \ldots,m$, committee $ A(i)$ and committee $ A(i \plus{} 1)$ have no member in common, where $ A(m \plus{} 1)$ denotes $ A(1);$
[i](iv)[/i] if $ 1 < |i \minus{} j| < m \minus{} 1,$ then committees $ A(i)$ and $ A(j)$ have at least one member in common.

Is it possible to have a cycle of 1990 committees with 11 countries?

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Source and history

task_id
753066bf-513e-5a46-857f-532e71ee5866
task_key
test--753066bf-513e-5a46-857f-532e71ee5866
task_revision_id
1
config / split
/ test

Official source

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