CHAPTER IV. 



GEOMETRICAL RECREATIONS CONTINUED. 



Leaving now the question of formal geometrical proposi- 

 tions, I proceed to enumerate a few games or puzzles which 

 depend mainly on the relative position of things, but I post- 

 pone to chapter X the discussion of such amusements of 

 this kind as necessitate any considerable use of arithmetic or 

 algebra. Some writers regard draughts, solitaire, chess, and 

 such like games as subjects for geometrical treatment in the 

 same way as they treat dominoes, backgammon, and games 

 with dice in connection with arithmetic : but these discussions 

 require too many artificial assumptions to correspond with the 

 games as actually played or to be interesting. 



The amusements to which I refer are of a more trivial 

 description, and it is possible that a mathematician may like to 

 omit this chapter. In some cases it is difficult to say whether 

 they should be classified as mainly arithmetical or geometrical, 

 but the point is of no importance. 



Statical Games of Position. Of the innumerable statical 

 games involving geometry of position I shall mention only 

 three or four. 



Three-in-a-row. First, I may mention the game of three- 

 in-a-row, of which noughts and crosses, one form of merrilees, 

 and go-bang are well-known examples. These games are 

 played on a board — generally in the form of a square con- 

 taining n 2 small squares or cells. The common practice is for 

 one player to place a white counter or piece or to make a cross 

 on each small square or cell which he occupies : his opponent 



