Different notes on a trumpet are obtained by moving its three valves up and down. The given table indicates the eight possible positions for these three valves and a note that would sound if the valves were in the indicated position. Is it possible to play one of these notes and then, by changing only one valve at a time, to play all the other notes without repeating a note twice? (Hint: Consider the notes as the objects of a set and that two notes are related if one can be obtained from the other by moving only one valve.)
Valve 1 | Valve 2 | Valve 3 | Note |
Up | Up | Up | C |
Up | Up | Down | A |
Up | Down | Up | B |
Up | Down | Down | Eb |
Down | Up | Up | F |
Down | Up | Down | D |
Down | Down | Up | E |
Down | Down | Down | C# |
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