Re: Partial Credit ;-)
Response To:
Re: Partial Credit ;-) ()

Alex Y

Each time the minute and hour hands are coincident, the second hand is at 12:00.

At 3:16 4/11, the second hand is between 4 and 5 (approx 22 seconds).

Here they will all be coincident at 12:00:00. That may be the only time when all are lined up, but I am not sure.

Yes, noon and midnight are the only two times when all three hands will be aligned. You have shown the other ten times each twelve hours when the minute and hour hands coincide, and can show that the second hand is not in the same place.

For Q1, think of the minute hand and hour hand running a race. The minute hand completes 24 "laps" around the clock face while the hour hand completes 2 "laps", so the minute hand "laps" the hour hand 22 times. No need to determine where those passes occur if there is no Q2.

I also wondered about the word "aligned" in this puzzle. Does it mean "oriented the same direction" [I think this is what it means] or does it mean "colinear"? If you give it the second definition, I think that the answer is 46 times.

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