yyGrams logoyyGrams/shortcuts

Shortcuts (theorems)

Players have discovered shortcuts for reducing yy-grams. These also help in recognizing equivalent solutions when a disagreement arises. Overall, remember that only inside-outside matters; serial order is not important. For example, ( ) g is equivalent to g ( )—that is, their outcome-lists are identical, in the sense of two people having identical shopping lists but in different order.

g.1 ((a)) = a

g.2 (a r)r = (a)r

g.3 ( )a = ( )

g.4 (( )a) =

g.5 (a)a = ( )

g.6 a a = a

g.7 ((a r)(b r)) = ((a)(b))r

h.1 Part of the fun is to recognize equivalent yy-grams. For example, advanced players recognize that

    (((z)i)g) = ((i)g)(z g).