A Room square, named after Thomas Gerald Room, is an n × n array filled with n + 1 different symbols in such a way that:
- Each cell of the array is either empty or contains an unordered pair from the set of symbols
- Each symbol occurs exactly once in each row and column of the array
- 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:
| 0,7 | 1,5 | 4,6 | 2,3 | |||
| 3,4 | 1,7 | 2,6 | 0,5 | |||
| 1,6 | 4,5 | 2,7 | 0,3 | |||
| 0,2 | 5,6 | 3,7 | 1,4 | |||
| 2,5 | 1,3 | 0,6 | 4,7 | |||
| 3,6 | 2,4 | 0,1 | 5,7 | |||
| 0,4 | 3,5 | 1,2 | 6,7 |
It is known that a Room square (or squares) exist if and only if n is odd but not 3 or 5.
Read more about Room Square: History, Applications, See Also
Famous quotes containing the words room and/or square:
“Behind her was confusion in the room,
Of chairs turned upside down to sit like people
In other chairs, and something, come to look,
For every room a house has parlor, bedroom,
And dining room thrown pell-mell in the kitchen.”
—Robert Frost (1874–1963)
“The square dance fiddler’s first concern is to carry a tune, but he must carry it loud enough to be heard over the noise of stamping feet, the cries of the “caller,” and the shouts of the dancers. When he fiddles, he “fiddles all over”; feet, hands, knees, head, and eyes are all busy.”
—State of Oklahoma, U.S. public relief program (1935-1943)