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Omni-MATH / The elevator buttons in Harvard's Science Center form a 3×2 grid of identical buttons, and each button lights up when pressed. One day, a student is in the elevator when all the ot…

Problem

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problem

The elevator buttons in Harvard's Science Center form a 3×23 \times 2 grid of identical buttons, and each button lights up when pressed. One day, a student is in the elevator when all the other lights in the elevator malfunction, so that only the buttons which are lit can be seen, but one cannot see which floors they correspond to. Given that at least one of the buttons is lit, how many distinct arrangements can the student observe? (For example, if only one button is lit, then the student will observe the same arrangement regardless of which button it is.)
Plain-text mathematical notation (without MathML)
The elevator buttons in Harvard's Science Center form a 3×2 grid of identical buttons, and each button lights up when pressed. One day, a student is in the elevator when all the other lights in the elevator malfunction, so that only the buttons which are lit can be seen, but one cannot see which floors they correspond to. Given that at least one of the buttons is lit, how many distinct arrangements can the student observe? (For example, if only one button is lit, then the student will observe the same arrangement regardless of which button it is.)
Original LaTeX notation
The elevator buttons in Harvard's Science Center form a $3 \times 2$ grid of identical buttons, and each button lights up when pressed. One day, a student is in the elevator when all the other lights in the elevator malfunction, so that only the buttons which are lit can be seen, but one cannot see which floors they correspond to. Given that at least one of the buttons is lit, how many distinct arrangements can the student observe? (For example, if only one button is lit, then the student will observe the same arrangement regardless of which button it is.)

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Source and history

task_id
7e1bf5d6-5f92-5340-a6c2-53de97fc2d77
task_key
test--7e1bf5d6-5f92-5340-a6c2-53de97fc2d77
task_revision_id
1
config / split
/ test

Official source

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