Survo Puzzle

Survo puzzle is a kind of logic puzzle presented (in April 2006) and studied by Seppo Mustonen.The name of the puzzle is associated to Mustonen's Survo system which is a general environmentfor statistical computing and related areas.

In a Survo puzzle the task is to fill an "m" × "n" table by integers1,2,...,"m"·"n" so that each of these numbers appears only once and theirrow and column sums are equal to integers given on the bottom and theright side of the table. Often some of the integers are given readily inthe table in order to guarantee uniqueness of the solution and/or formaking 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,...,9and the size of puzzle grid is typically very small.Solving Survo puzzles is also related to making of magic squares.

The degree of difficulty in solving Survo puzzles is strongly varying.Easy puzzles, meant for school children are pure exercises in addition andsubtraction, while more demanding ones require also good logic reasoning.The hardest Survo puzzles cannot be solved without computers.

Certain properties of Survo system like editorial computingand 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 magazineof the University of Helsinki from September 2006.

Example

Here is a simple Survo puzzle with 3 rows and 4 columns:

implying that the last number in the last row will be 30 - 7 - 9 -3 = 11:

Thus basic arithmetics and simple reasoning is enough for solvingeasy Survo puzzles like this one.

Properties of Survo puzzles

The rules of Survo puzzles are simpler than those of Sudoku.The grid is always rectangular or square and typically muchsmaller than in Sudoku and Kakuro.

The solving strategies are varying depending on the difficultyof the puzzle.In their simplest form, as in the following 2 × 3 case (degree of difficulty 0)

which makes the task almost trivial (degree of difficulty 0).

Assessing degree of difficulty

Measuring the degree of difficulty is based onthe number of 'mutations' needed by the first solver programmade by Mustonen in April 2006. This program works by usinga partially randomized algorithm.

The program starts by inserting the missing numbers randomly in thetable and tries then to get the computed sums of rows and columns as close to thetrue ones as possible by exchanging elements in the table systematically.This trial leads either to a correct solution or (as in most cases) to dead endwhere the discrepancy between computed and true sums cannot be diminishedsystematically. In the latter case a 'mutation' is made by exchanging two or morenumbers randomly. Thereafter the systematic procedure plus mutation is repeateduntil a true solution is found.In most cases, the mean number of mutations works as a crude measure for thelevel of difficulty of solving a Survo puzzle. This measure (MD) is computed as themean number of mutations when the puzzle is solved 1000 times by starting froma randomized table.The distribution of the number of mutations comes close to a geometric distribution.

These numeric values are often converted to a 5-star scale as follows:

MD

is solved by 5 swaps. The initial setup is

and the solution is found by swaps (7,9) (10,12) (10,11) (15,16) (1,2).In the Survo system, a sucro /SP_SWAP takes care of bookkeepingneeded in the swapping method.

Quick games

Solving of a hard Survo puzzle can take several hours.Solving Survo puzzles as quick games offers another kind of challenges.The most demanding form of a quick game is available in the netas a Java applet.

In this quick game, open 5 × 5 puzzles are solved by selecting (or guessing)the numbers by mouse clicks. A wrong choice evokes a melodic musical interval.Its range and direction indicate the quality and the amount of the error.The target is to attain as high score as possible.The score grows by correct choices and it is decreased by wrong ones andby the time used for finding the final solution.

See also

*Sudoku
*Kakuro
*Magic square

External links

* [http://www.survo.fi/puzzles Survo puzzles]
* [http://www.survo.fi/papers/enum_survo_puzzles.pdf Enumeration of Survo puzzles]
* [http://www.survo.fi/puzzles/swapm.html Swapping method]
* [http://www.survo.fi/java/quick5x5.html Quick game]