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Omni-MATH / An apartment building consists of 20 rooms numbered 1,2,…,20 arranged clockwise in a circle. To move from one room to another, one can either walk to the next room clockwise (i.e. …

Problem

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problem

An apartment building consists of 20 rooms numbered 1,2,…,201,2, \ldots, 20 arranged clockwise in a circle. To move from one room to another, one can either walk to the next room clockwise (i.e. from room ii to room $(i+1)(\bmod 20))$ or walk across the center to the opposite room (i.e. from room ii to room $(i+10)(\bmod 20))$. Find the number of ways to move from room 10 to room 20 without visiting the same room twice.
Plain-text mathematical notation (without MathML)
An apartment building consists of 20 rooms numbered 1,2,…,20 arranged clockwise in a circle. To move from one room to another, one can either walk to the next room clockwise (i.e. from room i to room $(i+1)(\bmod 20))$ or walk across the center to the opposite room (i.e. from room i to room $(i+10)(\bmod 20))$. Find the number of ways to move from room 10 to room 20 without visiting the same room twice.
Original LaTeX notation
An apartment building consists of 20 rooms numbered $1,2, \ldots, 20$ arranged clockwise in a circle. To move from one room to another, one can either walk to the next room clockwise (i.e. from room $i$ to room $(i+1)(\bmod 20))$ or walk across the center to the opposite room (i.e. from room $i$ to room $(i+10)(\bmod 20))$. Find the number of ways to move from room 10 to room 20 without visiting the same room twice.

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Source and history

task_id
c960d056-2cb1-563f-9986-c929bb69c7b7
task_key
test--c960d056-2cb1-563f-9986-c929bb69c7b7
task_revision_id
1
config / split
/ test

Official source

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