³. B´±µ¶·´±µ¸¹º

±.±

Game Trees

Consider the following simple two-player game

played on an

square grid

with a border of squares; let’s call the players Horace Fahlberg-Remsen and

Vera Rebaudi.

Each player has

tokens that they move across the board from

one side to the other. Horace’s tokens start in the left border, one in each row,

and move

hor

izontally to the right; symmetrically, Vera’s tokens start in the

top border, one in each column, and move

ver

tically downward. The players

alternate turns. In each of his turns, Horace either

moves

one of his tokens one

step to the right into an empty square, or

jumps

one of his tokens over exactly

one of Vera’s tokens into an empty square two steps to the right. If no legal

moves or jumps are available, Horace simply passes. Similarly, Vera either moves

or jumps one of her tokens downward in each of her turns, unless no moves or

jumps are possible. The ﬁrst player to move all their tokens oﬀ the edge of the

board wins. (It’s not hard to prove that as long as there are tokens on the board,

at least one player can legally move, and therefore someone eventually wins.)

Figure ±.´.

Vera wins the ±

± fake-sugar-packet game.

I don’t know what this game is called, or even if I’m reporting the rules correctly; I learned

it (or something like it) from Lenny Pitt, who recommended playing it with fake-sugar packets at

restaurants.

Constantin Fahlberg and Ira Remsen synthesized saccharin for the ﬁrst time in ±²¹², while

Fahlberg was a postdoc in Remsen’s lab investigating coal tar derivatives. In ±µ··, Ovidio Rebaudi

published the ﬁrst chemical analysis of

ka’a he’ê

, a medicinal plant cultivated by the Guaraní for

more than ±¶·· years, now more commonly known as

Stevia rebaudiana

³·