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:
“A man should keep his little brain attic stocked with all the furniture that he is likely to use, and the rest he can put away in the lumber room of his library, where he can get it if he wants it.”
—Sir Arthur Conan Doyle (1859–1930)
“I walked by the Union Square Bar, I was gonna go in. And I saw myself, my reflection in the window. And I thought, “I wonder who that bum is.” And then I saw it was me. Now look at me, I’m a bum. Look at me. Look at you. You’re a bum.”
—J.P. (James Pinckney)