# 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 add up to 15. This game is usually played by having players alternately select one of the remaining numbers from a pile which contains the numbers 1 to 9 at the outset. The player wins who first collects a triad of the numbers adding up to 15.

Although the games are mathematically equivalent, they are likely to differ psychologically, because they require different sorts of information. Number Scrabble is a numerical game requiring addition and subtraction of numbers, whereas Tic-Tac-Toe requires a spatial representation, which can only be disposed of with some difficulty, even by fairly experienced players. One the other hand, it is very easy, though maybe not likely to happen, to have one's 'moves' in Number Scrabble deteremed by super-imposing it on the Tic-Tac-Toe configuration, thus using the spatial magic square.

## Notes:

4 |
3 |
8 |

9 |
5 |
1 |

2 |
7 |
6 |

**Folksonomies:** math games number scrabble tic-tac-toe

**Taxonomies:**

/hobbies and interests/games/board games and puzzles (0.494249)

/hobbies and interests/magic and illusion (0.184553)

/hobbies and interests/games/lottery (0.169410)

**Keywords:**

Number Scrabble (0.944125 (negative:-0.235500)), magic square (0.737131 (neutral:0.000000)), fairly experienced players (0.734836 (positive:0.440121)), spatial magic square (0.716727 (neutral:0.000000)), Numerical Tic-Tac-Toe (0.698755 (neutral:0.000000)), Tic-Tac-Toe configuration (0.623929 (neutral:0.000000)), clear what heuristics (0.577844 (neutral:0.000000)), sufficient problems (0.575414 (neutral:0.000000)), main diagonals (0.573975 (neutral:0.000000)), psychological research (0.564799 (neutral:0.000000)), isomorphic game (0.556816 (negative:-0.235500)), spatial representation (0.552687 (neutral:0.000000)), different sorts (0.549150 (neutral:0.000000)), numerical game (0.526220 (neutral:0.000000)), numbers (0.473766 (negative:-0.573226)), outset (0.372133 (negative:-0.573226)), problem-solving (0.365039 (neutral:0.000000)), subtraction (0.364709 (neutral:0.000000)), opponent (0.362183 (negative:-0.530493)), investigator (0.360884 (neutral:0.000000)), triad (0.359170 (neutral:0.000000)), pile (0.357360 (negative:-0.573226)), difficulty (0.354673 (neutral:0.000000)), moves (0.352707 (neutral:0.000000)), subjects (0.351992 (neutral:0.000000)), fact (0.351002 (neutral:0.000000)), addition (0.350624 (neutral:0.000000)), columns (0.350291 (neutral:0.000000))

**Entities:**

investigator:JobTitle (0.753313 (neutral:0.000000))

**Concepts:**

Mathematics (0.961868): dbpedia | freebase | opencyc

Real number (0.916685): dbpedia | freebase | opencyc

Number (0.704917): dbpedia | freebase

Psychology (0.673732): dbpedia | freebase | opencyc

Subtraction (0.631047): dbpedia | freebase

Addition (0.592763): dbpedia | freebase

Elementary arithmetic (0.555112): dbpedia | freebase

Numbers (0.537113): dbpedia

Player (0.536200): dbpedia

Arithmetic (0.504051): dbpedia | freebase | opencyc

0 (0.496401): dbpedia | freebase | opencyc | yago

Multiplication (0.484940): dbpedia | freebase

Group (0.484078): dbpedia | freebase

Philosophy of science (0.470082): dbpedia | freebase

Play (0.454597): dbpedia | freebase | opencyc

Philosophy (0.442125): dbpedia | freebase | opencyc

Set theory (0.437963): dbpedia | freebase | opencyc

Problem solving (0.434076): dbpedia | freebase

Metaphysics (0.431508): dbpedia | freebase | opencyc

Social sciences (0.416083): dbpedia | opencyc

Natural number (0.415388): dbpedia | freebase | opencyc

Infinity (0.411208): dbpedia | freebase

Vector space (0.410406): dbpedia | freebase | yago

Plus and minus signs (0.408593): dbpedia | freebase

Greek loanwords (0.408463): dbpedia

Learning (0.404195): dbpedia | freebase | opencyc

Exponentiation (0.398522): dbpedia | freebase

Players (0.392729): dbpedia

Abstract algebra (0.392705): dbpedia | freebase

**The Game of JAM: An Isomorph of Tic-Tac-Toe**

**Periodicals>**

**Journal Article:**Michon, John A. (March 1967)

*, The Game of JAM: An Isomorph of Tic-Tac-Toe*, The American Journal of Psychology , Vol. 80, No. 1, Mar., 1967, Retrieved on 2016-12-24

**Folksonomies:**math math games