Question

For the Generate and Test problem solving method good generators are complete, non-redundant, and use useful information to restrict the number of possible solutions. In the burglar problem described below, suppose that the burglar knows the following information respectively, please estimate the average time that a wise burglar who may open the safe:
a) the second digit is 5, other digits are even
b) the first digit is even, the sum of the last three digits is 12.

Generate-and-Test systems often Do Identification To use the generate-and-test to identify, say, a tree, you can reach for a tree book, then thumb through it page by page, stopping when you find a picture that looks like the tree to be identified. Thumbing through the book is the generation procedure matching the pictures to the tree is the testing procedure. To use generate and test to burgle a three-number, two-digit safe, you can start with the combination 00-00-00, move to 00-00-01, and continue on through all possible combinations until the door opens. Of course, the counting is the generation procedure and the twist of the safe handle is the testing procedure. The burglar in figure 3.2 may take some time to crack the safe with this approach, however, for there are 100 1 million combinations. At three per minute, figuring that he will have to go through half of the com- binations, on average, to succeed, the job will take about 16 weeks, if he works 24 hours per day.

Answer 1

So, general six digits are there, where in the second digit is 5 and the other digits are even So now at are area one digit is constant that is 5, other digits are even approach 0, 2, 4, 6, 8 so 1, 3, 5, 7, 9 can not come at other 5 locations for combination this possible quantity of mixtures will be 65 = 7776 So time taken will be ((7776/360 = 43.2 Hrs In this case the first digit is even and the sum of last three digits is 12 So for closing 3 digits there are 19 ways we are to produce sum 12, Now the wide variety of possibilities can be 5* 19* 100 = 9500 So time taken maybe ((9500/3)/60) = 52.78 Hrs