Survo Puzzle - Assessing Degree of Difficulty

Assessing Degree of Difficulty

Measuring the degree of difficulty is based on the number of 'mutations' needed by the first solver program made by Mustonen in April 2006. This program works by using a partially randomized algorithm.

The program starts by inserting the missing numbers randomly in the table and tries then to get the computed sums of rows and columns as close to the true 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 end where the discrepancy between computed and true sums cannot be diminished systematically. In the latter case a 'mutation' is made by exchanging two or more numbers randomly. Thereafter the systematic procedure plus mutation is repeated until a true solution is found. In most cases, the mean number of mutations works as a crude measure for the level of difficulty of solving a Survo puzzle. This measure (MD) is computed as the mean number of mutations when the puzzle is solved 1000 times by starting from a 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

The degree of difficulty given as an MD value is rather inaccurate and it may be even misleading when the solution is found by clever deductions or by creative guesswork. This measure works better when it is required that the solver also proves that the solution is unique.