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## Find the Keyless Entry Number - Answer

Diana's car entry code is 39876.

Concentrate on the digits which have multiple potential matches per position because there are 10 numbers listed, but the access code is only 5 digits long. That means 5 of the random numbers in the list must be duplicates or triplicates so they can be ignored..

The first digit in random number list does not have any duplicates... It must be left to the end to solve.

The second digit has 4's and 9's duplicated.

The third digit has 1's triplicated and 8's duplicated.

The forth digit has 3's duplicated and 7's triplicated.

The last digit has 1's, 2's and 6's duplicated.

Because the first digit has no duplicates, one or more triplicates must be used.

Because the 9th random number, 98174 uses both triplicates digits, we know that the answer cannot contain xx17x, but must be either xx13x or xx87x because we know that the other digit positions must all be duplicates. In other words, the solution will contain 1 unduplicated row (the first row), 3 duplicated rows, and 1 triplicated row.

The 5th random row, 63136 contains both the 1 and 3, leaving us with xx87x as the only possible solution.

By keeping track of which rows have been used, and which columns contain duplicates that must be used, the two duplicates are quickly found: x9876.

This leaves the 7th row which has not been used, which results in the final answer:

39876

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