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Reality TV Problem

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Reality TV Problem

All the integers from zero to nine are contestants on the new reality TV show, "The Digital Age." Every week a new problem is posed, and any digit which cannot "solve" the problem is booted off the show. Below are the questions. Which digit will win?

I am a side of a triangle, and my other two side lengths are 4 and 5. 

I am not the last digit in any perfect square.

I am not a solution of x2 - 14x + 48 = 0.

If all the digits still in the game are multiplied together, I am not a digit of the result.

If all the digits which are no longer in the game are added together, I am a digit of the result.

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Problem by Mr. Twitchell

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