Find all integers n such that when the clock strikes n o'clock, the acute angle between the hour and minute hands is 90 degrees.
When a clock stricks on the hour, the minute hand has to be on the 12.
The only two places the hour hand can be to make a 90o angle are on the 3 or the 9.
edited to add.... The above assumes a 12-hour clock. If it's a 24-hour clock, you can figure it out the same way.