  We introduce CUT, the class of 2-player partition games. These are NIM type
games, played on a finite number of heaps of beans. The rules are given by a
set of positive integers, which specifies the number of allowed splits a player
can perform on a single heap. In normal play, the player with the last move
wins, and the famous Sprague-Grundy theory provides a solution. We prove that
several rulesets have a periodic or an arithmetic periodic Sprague-Grundy
sequence (i.e. they can be partitioned into a finite number of arithmetic
progressions of the same common difference). This is achieved directly for some
infinite classes of games, and moreover we develop a computational testing
condition, demonstrated to solve a variety of additional games. Similar results
have previously appeared for various classes of games of take-and-break, for
example octal and hexadecimal; see e.g. Winning Ways by Berlekamp, Conway and
Guy (1982). In this context, our contribution consists of a systematic study of
the subclass `break-without-take'.
