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?

(In reply to Part I solution by Bob Smith)

The only thing I see that may be a problem is the way you represent  roman numeral four.  On our granfather clock four is IV, not IIII.  I am looking for a way to do what the problem asks without the IIII, but Bob you did very well finding a solution thusfar.  :-)

Posted by Dan on 2006-03-27 13:32:14