enigma1369.txt (c) 2006 by Charles Petzold
"Magic Spell" by Susan Denham, New Scientist, 3 December 2005, page 56
A wheel of 24 lights each with a letter (except X and Z) spells out words.
The wheel is said to have a diameter that is "a whole number of centimeters."
For the words indicated in the puzzle, it is said that "the distance
between any one flashing light and the next was a whole number of centimeters."
How can this be so? Think of the 24 lights as divided into 4 groups of 6, so
going around the circumference the lights can be labeled Group 1, Group 2,
Group 3, Group 4, Group 1, Group 2, Group 3, Group 4, and so forth.
Each group forms a hexagon. If the diameter is 2N, then the distance between
adjacent lights in a group is N.
So we're really looking for a way to distribute 24 letters among 4 groups,
where each group is ordered and certain sequences within each group spell
out words.
We are given that Group 1 contains the letters ENIGMA in that order.
The letters are the vertices of a hexagon. We can also spell out NINE in this
group, and also MAINE. Notice that for MAINE, we make jumps of distance
N (from M to A), 2N (from A to I), and then two more N jumps.
I don't see any more numbers, or months of the year, or former American
presidents in that group, so these will be in other groups. Uncovering
possibilities should be easy because we don't have access to the vowels
A, E, or I, and we as N, G, or M.
The month is JULY. The number could be FOUR (but that wouldn't work with JULY)
or TWO. The President could be BUSH (but that wouldn't work with JULY)
or POLK (but that wouldn't work with JULY either) so it has to be FORD.
So, the second group contains JULY, and the third group is the letters
TWORDF. We can spell TWO easily enough and also FORD by making an initial
jump of 2N.
Answer: JULY, FORD, MAINE, TWO, and NINE.