|
A Survo puzzle is a kind of logic puzzle presented (in April 2006) and studied by Seppo Mustonen.〔 Aitola, Kerttu (2006): "Survo on täällä" ("Survo is here"). ''Yliopisto'' 54(12): 44–45.〕 The name of the puzzle is associated with Mustonen's Survo system, which is a general environment for statistical computing and related areas.〔 Mustonen, Seppo (2007): ("Survo Crossings" ). ''CSCnews'' 1/2007: 30–32.〕 In a Survo puzzle, the task is to fill an ''m'' × ''n'' table with integers 1, 2, ..., ''m''·''n'' so that each of these numbers appears only once and their row and column sums are equal to integers given on the bottom and the right side of the table. Often some of the integers are given readily in the table in order to guarantee uniqueness of the solution and/or for making the task easier.〔 To some extent, Survo puzzles resemble Sudoku and Kakuro puzzles. However, numbers used in the solution are not restricted to 1, 2, ..., 9 and the size of puzzle grid is typically very small. Solving Survo puzzles is also related to making of magic squares.〔 Vehkalahti, Kimmo (2007): ("Some comments on magic squares and Survo puzzles" ). The 16th International Workshop on Matrices and Statistics, University of Windsor, Canada, June 1–3, 2007.〕 The degree of difficulty in solving Survo puzzles is strongly varying. Easy puzzles, meant for school children, are pure exercises in addition and subtraction, while more demanding ones require also good logic reasoning. The hardest Survo puzzles cannot be solved without computers.〔 Mustonen, Seppo (2007): ("On Survo cross sum puzzles" ). In J. Niemelä, S. Puntanen, and E. P. Liski (eds.) ''Abstracts of the Annual Conference of Finnish Statisticians 2007, "Multivariate Methods"'', pp. 23–26. Dept. of Mathematics, Statistics and Philosophy, University of Tampere. ISBN 978-951-44-6957-2.〕 Certain properties of the Survo system like editorial computing and the COMB operation, making e.g. restricted integer partitions, support solving of Survo puzzles. Survo puzzles have been published regularly in Finland by ''Ilta-Sanomat'' and the scientific magazine of the University of Helsinki from September 2006. Solving of Survo puzzles was one of the three main topics in the national entrance examination of the Finnish universities in computer science (2009).〔 ("Tietojenkäsittelytieteen yhteisvalinta 22.5.2009, Tehtävä 3: Survo-ristikko" ). ("National entrance examination in computer science, May 22nd 2009, Exercise 3: Survo Puzzle").〕 == Example == Here is a simple Survo puzzle with 3 rows and 4 columns: Numbers 3, 6, and 8 are readily given. The task is to put remaining numbers of 1-12 (3×4=12) to their places so that the sums are correct. The puzzle has a unique solution found stepwise as follows: The missing numbers are 1,2,4,5,7,9,10,11,12. Usually it is best to start from a row or a column with fewest missing numbers. In this case columns A, B, and C are such. Column A is not favorable since the sum 19 of missing numbers can be presented according to the rules in several ways (e.g. 19 = 7 + 12 = 12 + 7 = 9 + 10 = 10 + 9). In the column B the sum of missing numbers is 10 having only one partition 10 = 1 + 9 since the other alternatives 10 = 2 + 8 = 3 + 7 = 4 + 6 are not accepted due to numbers already present in the table. Number 9 cannot be put in the row 2 since then the sum of this row would exceed the value 18. Therefore the only choice is to start the solution by Now the column A has only one alternative 27 - 8 = 19 = 7 + 12 = 12 + 7. Number 7 cannot be in the row 1 because the sum of missing numbers in that row would be 30 - 7 - 6 = 17 and this allows no permitted partition. Thus we have implying that the last number in the last row will be 30 - 7 - 9 -3 = 11: In the first row the sum of the missing numbers is 30 - 12 - 6 = 12. Its only possible partition is 12 = 2 + 10 and so that number 2 will be in the column C; 10 in this position is too much for the column sum. The solution is then easily completed as Thus basic arithmetics and simple reasoning is enough for solving easy Survo puzzles like this one. 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「Survo puzzle」の詳細全文を読む スポンサード リンク
|