13

Part of 2013 Stanford Mathematics Tournament

Problems(2)

2013 General Problem 13

Source:

\mathbb{R}^2

-tic-tac-toe is a game where two players take turns putting red and blue points anywhere on the

xy

plane. The red player moves first. The first player to get

3

of their points in a line without any of their opponent's points in between wins. What is the least number of moves in which Red can guarantee a win? (We count each time that Red places a point as a move, including when Red places its winning point.)

SMT 2013 Team #13

Source:

2

4

6

written on it. A person repeatedly selects (not necessarily distinct) values for

x

y

z

from the board, and writes down

xyz+xy+yz+zx+x+y+z

if and only if that number is not yet on the board and is also less than or equal to

2013

. This person repeats this process until no more numbers can be written. How many numbers will be written at the end of the process?