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:
“No one asks you to throw Mozart out of the window. Keep Mozart. Cherish him. Keep Moses too, and Buddha and Lao tse and Christ. Keep them in your heart. But make room for the others, the coming ones, the ones who are already scratching on the window-panes.”
—Henry Miller (1891–1980)
“After the planet becomes theirs, many millions of years will have to pass before a beetle particularly loved by God, at the end of its calculations will find written on a sheet of paper in letters of fire that energy is equal to the mass multiplied by the square of the velocity of light. The new kings of the world will live tranquilly for a long time, confining themselves to devouring each other and being parasites among each other on a cottage industry scale.”
—Primo Levi (1919–1987)