"Let me walk you through one of these," Inez says. "Just so you can see how it works. We'll start with the second grid:
"… and select Square k (which is the same as selecting its mirror image, m, since any strategy that works against k will work against m as well):
"With an X in Square k, O has no choice but to take Square q:
(The exclamation point in these diagrams indicates a square that the player had no choice but to take.)
"X now has 5 remaining squares to choose from – l, m, o, p, and q – and O hasn't set up any structures that X needs to block. You'd think that this gives X free choice, but watch what happens if X takes Square l:
"This forces O to take Square p:
". . . which sets up a fork for O. X would have to take both Square m and Square r to keep O from winning:
"According to our rules of perfect play, therefore, X cannot take Square l because that creates a fork for O."
"This leaves X with four remaining options for their third move: m, o, p, and r:
"If O can get a fork with each of these other four options, then X taking k (or m) on their second move guarantees O the win. Is that the case?"
You stare down at the napkin, frowning.
"Once you've figured all of that out," Inez says, "you have to do a similar analysis for X's other five options for a second move."
You can determine the answer to Inez's question and find that number on the Solution List. Or you can