Editing Soma cube (section)

==Solutions==
[[File:Soma_cube_puzzle_solution.svg|thumb|One of the possible ways of assembling the Soma cube]]
Solving the Soma cube has been used as a task to measure individuals' performance and effort in a series of psychology experiments. In these experiments, test subjects are asked to solve a soma cube as many times as possible within a set period of time. For example, In 1969, [[Edward Deci]], a Carnegie Mellon University graduate assistant at the time,<ref>Pink, Daniel H. (2009). "Drive, The Surprising Truth About What Motivates Us". Riverhead Books.</ref> asked his research subjects to solve a soma cube under conditions with varying incentives in his dissertation work on [[intrinsic motivation|intrinsic]] and [[extrinsic motivation|extrinsic]] motivation establishing the [[social psychological]] theory of [[Motivation crowding theory|crowding out]].

In each of the 240 distinct solutions to the cube puzzle, there is only one place that the "T" piece can be placed. Each solved cube can be rotated such that the "T" piece is on the bottom with its long edge along the front and the "tongue" of the "T" in the bottom center cube (this is the normalized position of the large cube). This can be proven as follows: If you consider all the possible ways that the "T" piece can be placed in the large cube (without regard to any of the other pieces), it will be seen that it will always fill either two corners of the large cube or zero corners. There is no way to orient the "T" piece such that it fills only one corner of the large cube. The "L" piece can be oriented such that it fills two corners, or one corner, or zero corners. Each of the other five pieces have no orientation that fills two corners; they can fill either one corner or zero corners. Therefore, if you exclude the "T" piece, the maximum number of corners that can be filled by the remaining six pieces is seven (one corner each for five pieces, plus two corners for the "L" piece). A cube has eight corners. But the "T" piece cannot be oriented to fill just that one remaining corner, and orienting it such that it fills zero corners will obviously not make a cube. Therefore, the "T" must always fill two corners, and there is only one orientation (discounting rotations and reflections) in which it does that. It also follows from this that in all solutions, five of the remaining six pieces will fill their maximum number of corners and one piece will fill one fewer than its maximum (this is called the deficient piece).<ref name=":0">{{citation|url=http://www.fam-bundgaard.dk/SOMA/NEWS/N030518.HTM|title=The complete "SOMAP" is found|journal=SOMA News|first=William|last=Kustes|date=May 18, 2003|access-date=April 25, 2014}}.</ref>