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why is the minimunm numbers equal to n-1,

shouldnt it be n

]]>thanks very very much ]]>

This strategy is “optimal” in the following sense:

– The tree is minimal in the maximum depth of the tree (i.e. the number of trials required to know the answer).

– In the case of several trees that are optimal in the above property, it’s minimal in the average depth of the tree.

– In the case of several trees that are optimal in the above properties, submits a correct answer as often as possible.

I hope this formats correctly.

Try [0,0,0,0,0]. If the score is:

0 → The answer is [1,1,1,1,1].

1 → Try [0,0,0,1,1]. If the score is:

1 → Try [1,1,1,0,1]. If the score is:

3 → The answer is [1,1,1,1,0].

5 → The answer is [1,1,1,0,1].

3 → Try [0,1,1,1,1]. If the score is:

3 → Try [1,0,1,1,1]. If the score is:

3 → The answer is [1,1,0,1,1].

5 → The answer is [1,0,1,1,1].

5 → The answer is [0,1,1,1,1].

2 → Try [0,0,1,1,1]. If the score is:

1 → Try [1,1,0,0,1]. If the score is:

3 → Try [1,1,0,1,0]. If the score is:

3 → The answer is [1,1,1,0,0].

5 → The answer is [1,1,0,1,0].

5 → The answer is [1,1,0,0,1].

3 → Try [0,1,0,1,1]. If the score is:

1 → Try [1,0,1,0,1]. If the score is:

3 → The answer is [1,0,1,1,0].

5 → The answer is [1,0,1,0,1].

3 → Try [0,1,1,0,1]. If the score is:

1 → The answer is [1,0,0,1,1].

3 → The answer is [0,1,1,1,0].

5 → The answer is [0,1,1,0,1].

5 → The answer is [0,1,0,1,1].

5 → The answer is [0,0,1,1,1].

3 → Try [0,0,0,1,1]. If the score is:

1 → Try [0,1,1,0,0]. If the score is:

3 → Try [1,0,1,0,0]. If the score is:

3 → The answer is [1,1,0,0,0].

5 → The answer is [1,0,1,0,0].

5 → The answer is [0,1,1,0,0].

3 → Try [0,0,1,0,1]. If the score is:

1 → Try [0,1,0,1,0]. If the score is:

3 → The answer is [1,0,0,1,0].

5 → The answer is [0,1,0,1,0].

3 → Try [0,1,0,0,1]. If the score is:

1 → The answer is [0,0,1,1,0].

3 → The answer is [1,0,0,0,1].

5 → The answer is [0,1,0,0,1].

5 → The answer is [0,0,1,0,1].

5 → The answer is [0,0,0,1,1].

4 → Try [0,0,0,1,1]. If the score is:

2 → Try [0,0,1,0,0]. If the score is:

3 → Try [0,1,0,0,0]. If the score is:

3 → The answer is [1,0,0,0,0].

5 → The answer is [0,1,0,0,0].

5 → The answer is [0,0,1,0,0].

4 → Try [0,0,0,0,1]. If the score is:

3 → The answer is [0,0,0,1,0].

5 → The answer is [0,0,0,0,1].

5 → The answer is [0,0,0,0,0].

a(n) ≥ ⌈ n/⌈lg n⌉ ⌉

In particular:

a(5) ≥ 3

a(8) ≥ 4

a(30) ≥ 6

It may not be a terribly tight lower bound, but it’s a lower bound nonetheless.

Conjecture: For a test with n questions, if at each stage you are required to submit a test whose answers are consistent with all of the previous scores, you need to take the test n times to determine what all the answers are.

Now what if you had to submit all of your tests in advance, and so couldn’t use the results from a previous test to determine what answers to provide for the next test?

]]>http://en.wikipedia.org/wiki/Mastermind_%28board_game%29 ]]>

Read again what I have written. I never say that correct answer is “0 1 0” I have just made an assumption. Can’t explain the strategy until I choose one of the solutions. The strategy is applicable to 1 0 0 also…..

Assuming if the solution is 1 0 0, the 0 0 0 will give score of 2 and so automatically I know 1 1 1 (previous one’s complement) will give a score of 1.

0 0 1 will give a score of 1 and so it’s comlement 1 1 0 will give a score of 2.

Using these results and then applying similar analysis I can zero in on the solution.

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