Shrinking Squares and Colourful Cubes

摘要

The new puzzle this time is an easy one about cubes. But first we have to look at the nasty nested squares from last time. The numbers at the corner of an inner square are the differences between the numbers at the corners of the outer square. The sample shown was as below.In that example it took five iterations to get all zeroes. The question is what is the maximum number of iterations required? The overall brief answer is that it is unlimited. But it depends upon the ordering of the original numbers. There are three possibilities:1) Largest and smallest are opposite. 2) Largest and smallest adjacent, second next to largest. 3) Largest and smallest adjacent, second next to smallest. The example above is of type 3.