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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: It is known that a Room square (or squares) exist if and only if ''n'' is odd but not 3 or 5. ==History== The order-7 Room square was used by Robert Anstice to provide additional solutions to Kirkman's schoolgirl problem in the mid-19th century, and Anstice also constructed an infinite family of Room squares, but his constructions did not attract attention.〔.〕 Thomas Gerald Room reinvented Room squares in a note published in 1955,〔.〕 and they came to be named after him. In his original paper on the subject, Room observed that ''n'' must be odd and unequal to 3 or 5, but it was not shown that these conditions are both necessary and sufficient until the work of W. D. Wallis in 1973.〔. Also published in ''Historical Records of Australian Science'' 7 (1): 109–122, . An abridged version is (online at the web site of the Australian Academy of Science ).〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Room square」の詳細全文を読む スポンサード リンク
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