20 points) For the Generate and Test problem solving method good generators are

Question

20 points) 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 paradigm to identify, say, 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 A 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.

Explanation / Answer

S, total six digits are there,

a) in which the second digit is 5 and the other digits are even
So now at one place one digit is fixed which is 5, now other digits are even means 0, 2, 4, 6, 8, so 1, 3, 5, 7, 9 cannot come at other 5 places for combination this possible number of combinations will be= 65= 7776

So time taken will be ((7776/3)/60)= 43.2 Hrs

b) in this case, the first digit is even and the sum of last three digits is 12

So for last three digits there are 19 ways we can produce sum 12,

Now the number of posibilities will be 5*19*100= 9500

So time taken will be ((9500/3)/60)= 52.78 Hrs

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