Does anyone know how to solve this white rabbit pocket watch puzzle?

[royalenc]

The White Rabbit’s (12-hour) pocket watch is running very fast! And yet it always shows the correct time on the hour, every hour, and only on the hour. When Alice says, “It’s only half past one”, what time does the White Rabbit’s watch show?

 

[Deleted member 4993]

The White Rabbit’s (12-hour) pocket watch is running very fast! And yet it always shows the correct time on the hour, every hour, and only on the hour. When Alice says, “It’s only half past one”, what time does the White Rabbit’s watch show?

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[HallsofIvy]

The White Rabbit’s (12-hour) pocket watch is running very fast! And yet it always shows the correct time on the hour, every hour, and only on the hour. When Alice says, “It’s only half past one”, what time does the White Rabbit’s watch show?

It sounds like you are saying that the watch is running 13 hours forward every hour. That is, if it shows 12:00 at noon it would show 12:00+ 13 hours= 1:00 an hour later. How many hours forward will it have run in 30 minutes?

(This is assuming a 12 hour watch. If the White Rabbit's watch were a 24 hour watch (this wonderland, after all) the answer would be different.)

 

[royalenc]

It sounds like you are saying that the watch is running 13 hours forward every hour. That is, if it shows 12:00 at noon it would show 12:00+ 13 hours= 1:00 an hour later. How many hours forward will it have run in 30 minutes?

(This is assuming a 12 hour watch. If the White Rabbit's watch were a 24 hour watch (this wonderland, after all) the answer would be different.)

wonderful. Thanks a lot.

 

[Steven G]

It sounds like you are saying that the watch is running 13 hours forward every hour. That is, if it shows 12:00 at noon it would show 12:00+ 13 hours= 1:00 an hour later. How many hours forward will it have run in 30 minutes?

(This is assuming a 12 hour watch. If the White Rabbit's watch were a 24 hour watch (this wonderland, after all) the answer would be different.)

I think that you may be guilty of sloppy thinking. Why just 13 hours movement in 1 hour? How about 25 hours or 37 hours....?

 

[Dr.Peterson]

I think that you may be guilty of sloppy thinking. Why just 13 hours movement in 1 hour? How about 25 hours or 37 hours....?

If it went 25 hours per hour, I think there would be another time between hours (on the half hour, if I'm thinking correctly) when the time would be correct.

 

[Steven G]

If it went 25 hours per hour, I think there would be another time between hours (on the half hour, if I'm thinking correctly) when the time would be correct.

Thanks for informing me of that. I admit that I did not think of that (and hence I was guilty of sloppy thinking!--I hope Kahn doesn't see this). I have no idea how an arithmetic student could see that even if the watch moved 13 hours in an hour period that it only has the correct time on the hour. I have to think about what you said.

 

[Dr.Peterson]

As usual, we don't really know that the context allows only arithmetic; it may have been put there because nothing more is evident on the surface. I used graphical thinking to convince myself that more than 13 hours wouldn't work (and didn't answer sooner because I wasn't yet convinced my first time through).

But it's easy enough to see that no intermediate time would be correct at 13x speed, if you just imagine turning the clock forward: the hour will be wrong until you reach the end.