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**emerald000** · 08-4-2008, 05:18 PM

I guess I will post mine. It is 132 times, for those wondering.

In order to put it as simpler as possible, we'll start with the number of times in the 12

x range. We need to find times when we swap the hands, it is a correct time.

The first and easiest one is the 12:00. The only problem is that we know which one it is, because the hands are overlapped. So we don't count this one.

Then, let's analyze the 12:05 to 12:10 range. Since the minutes hand is between the 1 and the 2, the inverted time will have an time of 1

x, and the inverted minutes will be around 6-7. Note that if you take all the possibilities of the normal time (the infinite number of them), you will see that the inverted hour hand will take every position between the 1 and the 2. That way, it is sure to be in the good place once in its travel.

You can apply the same reasoning to every other 5 minutes on the clock, except one, which will be when the hands are overlapped. You can also apply that reasoning to the other 12 hours of the clock.

So, that gives: 12 hours x 11 times per hour = 132 times. (Note that the "11 times per hour" comes from the twelve 5-minutes in an hour minus the 5-minute in which the hands are overlapped)

Bow down to my superior intelligence.

PS: I would like to see your solution Rubix.

08-4-2008, 05:18 PM	#74
emerald000 the Mathemagician~ Join Date: Nov 2005 Location: Quebec City Age: 33 Posts: 1,320	Re: MrRubix's Riddle Thread I guess I will post mine. It is 132 times, for those wondering. In order to put it as simpler as possible, we'll start with the number of times in the 12x range. We need to find times when we swap the hands, it is a correct time. The first and easiest one is the 12:00. The only problem is that we know which one it is, because the hands are overlapped. So we don't count this one. Then, let's analyze the 12:05 to 12:10 range. Since the minutes hand is between the 1 and the 2, the inverted time will have an time of 1x, and the inverted minutes will be around 6-7. Note that if you take all the possibilities of the normal time (the infinite number of them), you will see that the inverted hour hand will take every position between the 1 and the 2. That way, it is sure to be in the good place once in its travel. You can apply the same reasoning to every other 5 minutes on the clock, except one, which will be when the hands are overlapped. You can also apply that reasoning to the other 12 hours of the clock. So, that gives: 12 hours x 11 times per hour = 132 times. (Note that the "11 times per hour" comes from the twelve 5-minutes in an hour minus the 5-minute in which the hands are overlapped) Bow down to my superior intelligence. PS: I would like to see your solution Rubix.