**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?

Numbers on grandfather clocks are written "radially", that is to say the center of the clockface is always the "down" direction.

That being the case, the rays can be drawn as such

1) split the X and I of the 11 o'clock position

2) between the counterclockwise-most I of 4 (IIII on grandfather clocks) and the rest

3) split the VI and I of the 7 o'clock position

4) split the I and X of the 9 o'clock position

Four sectors (sum the numerals)

rays 1-2) IXIIIIIIIII = 20

rays 2-3) IIIVVIVI = 20

rays 3-4) IVIIIIX = 20

rays 4-1) XX = 20