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Swap Time

Category:Math
Submitted By:Snowdog
Fun:*** (2.63)
Difficulty:*** (2.94)



This puzzle is split into an initial logic based piece and then a rigorous math piece, so everyone can play.

Picture a standard clock with continuously moving hour and minute hands.

A "Swap Time" is a time when you can swap the hour and minute hand, and still get a valid time.

For example, 3:00 is NOT a Swap Time. If we swap the minute hand and the hour hand, then the minute hand points directly at the 3 and the hour hand points directly at the 12. This is not a valid time. When the minute hand points at the three, the hour hand will not be pointing directly at any number.

A) Find one Swap Time.
B) What are the Swap Times between 1:00 and 2:00?

Times will be specified as hours, minutes, and seconds rounded to two decimal places.

Ignore a.m. and p.m. distinctions.

Bonus: How many Swap Times are there in total?

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