Number Scrabble: Numerical Tic-Tac-Toe

In psychological research on problem-solving, sometimes the game of Tic-Tac-Toe is employed, which, though very simple to learn and play, still offers sufficient problems to the investigator in that it is not at all clear what heuristics are used by the subjects, except avoiding the winning move of the opponent. The same is apparently true for the isomorphic game of Number Scrabble, which is based on the fact that there exists a 3 X 3 magic square, of which rows, columns, and main diagonals a...

 The Monty Hall Problem

Here’s how Monty’s deal works, in the math problem, anyway. (On the real show it was a bit messier.) He shows you three closed doors, with a car behind one and a goat behind each of the others. If you open the one with the car, you win it. You start by picking a door, but before it’s opened Monty will always open another door to reveal a goat. Then he’ll let you open either remaining door. Suppose you start by picking Door 1, and Monty opens Door 3 to reveal a goat. Now what should y...