**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)

Maybe you have one-a-them new-fangled grandfather clocks. :)

Web quote www.antiquegrandfatherclocks.com:

**Antique Grandfather Clock Dials**

Hands up those of you who own a grandfather clock which has roman numerals on the dial and have never noticed that the one of the numerals was wrong.? If you are honest,I expect that a lot of hands will reach for the sky.Have a look at the number 4.

In roman numerals it should be 1V but it is nearly always 1111.

I have discussed this point many times with my clock peers and we can only come up with the fact that 1111 balances out the dial better with the nmber V111 on the opposite side.If anyone amongst you knows of another reason ,I would be most delighted to hear it.