What The Method That Could/Should Be Used For This Type of Problem?

h0wb0y

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Nov 24, 2015
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Hello everyone. A friend presented me with a challenge to figure out how to come up with the math behind a particular game and it has me completely scratching my head. I have been doing quite a bit of searching - but I am finding that I can't even figure out what type of method could be searched on because I do not know what to call it.

The game is this:
Person A thinks of a 7 digit number from 0000000 to 9999999. The goal of Person B is to figure out that seven digit number in as few guesses as possible. When Person B makes a guess, Person A can only say how many numbers are correct and how many numbers are in the correct order (without specifically naming which numbers are correct and without specifically naming which numbers are in the correct order). Repeated numbers each count as individually 'correct' numbers (I.E. if Person A's number is 0000011 and Person B's guess is 1222221, Person A would state, "You have two numbers correct and one number in the correct place."

Now - this game is only played once a week with only one guess per week allowed - so, solid math behind this will obviously be a massive help.

The first run of the game is playing out as follows:
For the first guess, a person's phone number was chosen to be used as a baseline starting point (the next guesses and their results will be placed by each other to hopefully better allow visualization).
2506721 - which yielded 4 correct numbers and 2 numbers in the correct position
2536721 - which yielded 3 correct numbers and 1 number in the correct position
2006721 - which yielded 4 correct numbers and 2 numbers in the correct position
2102489 - which yielded 3 correct numbers and 2 numbers in the correct position

To me, this points to the fact that 0 has to be the 3rd digit. _ _ 0 _ _ _ _

To something else in the mix, it was accidentally slipped that there are no 3's in the number.

I know that the data already in place will yield more facts; however, I do not have any clue how to seek out how I really need to name this type of problem in order to begin researching it - so I am reaching out for help on here!
Surely there is a name for this exact type of problem, right? A calculator for it would be awesome - because what I would really like to see is how THAT calculator is computing the solution.

Thanks everyone!
 
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