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IMP SOLVE IT! Is It a Digit?

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There are five empty boxes shown here labeled 0 through 4. 01234

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The digit you put in the box labeled “0” must be the same as the number of 0’s you use. The digit you put in the box labeled “1” must be the same as the number of 1’s you use. The digit you put in the box labeled “2” must be the same as the number of 2’s you use, and so on… Your task is to put a digit 0 through 4 inside each of the boxes so that certain conditions hold: 012 34

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What to do What Not to Do You are allowed to use the same digit more than once. You may want to make several copies of the set of boxes in order to try the various combinations of digits. Here is an example of an incorrect way to fill the boxes. This is incorrect for many reasons. For instance, there is a 1 in the box labeled “2”, but there is more than one 2 in the boxes….. Additional Information 232 2 12

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POW 1 A Digital Proof Once you have solved the problem in Is it a Digit?, your task is to prove that you have all the solutions. Write Up 1. Problem Statement: Explain the problem from Is it a Digit? 2. Process: Based on your notes, describe how you went about finding all the solutions to Is it a Digit? And how you decided that you had them all. 3. Solutions: List all solutions you found for the Is it a Digit? Then write a careful and detailed proof that there are no solutions to Is it a Digit? other than those listed. 4. Evaluation 5. Self-assessment

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Warning!!!!!! The answer(s) follow on the following slide.

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The order of the numbers should be 21200 The proof that the solution is unique consists fo eliminating all other possibilities. However, there are so many possibilities (5 5 or 3125) the other cases need to be eliminated in an organized and systematic way. However, once 3 and 4 are eliminated, a proof could be made by showing the 3 3 or 27 possibilities. Also a proof can be shown that the digits must be equal to 5.

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