Drawback of Representation 1

Q: What is the largest pile size for which this representation will work?

A: 9

Q: How might we represent larger piles, as in:

?

     (define make-game-state
       (lambda (i j) (+ (* 100 i) j)))

     (define size-of-pile
       (lambda (game-state pile-number)
         (if (= pile-number 1)
             (quotient game-state 100)
             (remainder game-state 100))))
This data representation method puts an artificial restriction on the size of piles.

While this is acceptable for 2-pile Nim, other data types should not be subject to such a restriction.