I Draw the face of a clock numbered with roman numerals in the usual way. Explain how to draw 4 rays radiating from the center such that the sum of the numerals in each sector is 20.

II At what time are the two hands of a clock situated so that, reckoning in minutes from XII, one is exactly the square of the distance of the other?

III At what time between three and four o’clock is the minute hand the same distance from VIII as the hour hand is from XII?

I think the solution to part III is 3:23 and 30 seconds.  It was easy enough to figure that it would be at some point between 3:23 and 3:24, I used an Excel spreadsheet to work out the seconds.

As for the other two parts...I'm getting the nauseating feeling that Part II also requires the use of seconds, which is a pain.  I did a quick run of just hours and minutes and didn't find a solution, but I might have done something wrong.

Part I doesn't even make sense to me.  The numerals on a clock only add up to 78, so I don't see how you could create four regions each totaling 20.  There must be some trick, like having one of the rays divide an "I" into two halves or something...but even then I'm not sure how it could be done.

Back to the drawing board...

Posted by tomarken on 2006-03-27 13:09:09