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 re: Part I solution by Dan)

Whoa...haha, that is great!  I was missing that fact that when you sum the 12 values on the face you get 78 - but when you represent them as roman numerals the IX (which I so carelessly counted as 9) actually provides 11, which is where the extra 2 come from.  I was also going with the assumption that a 4 is represented as IV, which is the other problem I ran into.  Good job Bob!

Posted by tomarken on 2006-03-27 13:59:37