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 II solution by Bob Smith)

As the solution to I indicated that the grandfather clock in reference is an antique grandfather clock, I would assume there is no second hand -- (though there actually may have been the kind to exist).  My recollection is the periodic movement of the minute hand as it 'clicked' to the next interval after each lapse of 60 seconds timed by the 'tick-tock' swing of the pendulum.

Thus, the only time I see as a solution is 12 O'Clock where both the minute hand and the hour hand are at a distance of zero from the XII and from each other.
                                          0² = 0

Aha, I believe I have the answer....

At 2:24, the hour will be on the 12 minute mark, a distance of 12 minute marks from the XII, and  the minute hand will have travelled 12² = 144 minute marks.

I will say that both solutions are correct.

Edited on March 30, 2006, 10:50 pm

Posted by Dej Mar on 2006-03-27 22:33:14