Room square

A Room square, named after Thomas Gerald Room, is an n × n array filled with n + 1 different symbols in such a way that: 1. * Each cell of the array is either empty or contains an unordered pair from the set of symbols 2. * Each symbol occurs exactly once in each row and column of the array 3. * Every unordered pair of symbols occurs in exactly one cell of the array. An example, a Room square of order seven, if the set of symbols is integers from 0 to 7: It is known that a Room square (or squares) exist if and only if n is odd but not 3 or 5.

Room square

A Room square, named after Thomas Gerald Room, is an n × n array filled with n + 1 different symbols in such a way that: 1. * Each cell of the array is either empty or contains an unordered pair from the set of symbols 2. * Each symbol occurs exactly once in each row and column of the array 3. * Every unordered pair of symbols occurs in exactly one cell of the array. An example, a Room square of order seven, if the set of symbols is integers from 0 to 7: It is known that a Room square (or squares) exist if and only if n is odd but not 3 or 5.