536 Puzzles and Curious Problems

176 Combinatorial & Topological Problems

you exchange black number 3 with 4,

or with 5, or with 6, you get different

necklaces. But if you exchange 3 with

7 it will be the same as 3 with 5, be-

cause it is merely turning the necklace

over. So we have to beware of count-

ing such repetitions as different. The

answer is a much smaller one than

the reader may anticipate.

459. AN EFFERVESCENT PUZZLE

In how many different ways can the ever appearing together? Of course

letters in the word EFFERVESCES similar letters, such as FF, have no

be arranged in a line without two E's separate identity, so that to inter-

change them will make no difference.

5

:(

s

v

When the reader has done this he

should try the case where the letters

have to be arranged differently in a

circle, as shown, with no two E's to-

gether. We are here, of course, only

concerned with the order of the letters

and not with their positions on the

circumference, and you must always

read in a clockwise direction, as indi-

cated by the arrow.

460. TESSELLATED TILES

Here we have twenty tiles, all colored with the same four colors, and the
order of the coloring is indicated by the shadings: thus, the white may repre-
sent white; the black, blue; the striped, red; and the dotted, yellow.
The puzzle is to select any sixteen of these tiles that you choose and arrange
them in the form of a square, always placing similar colors together-white
against white, red against red, and so on. It is quite easy to make the squares