## June 2007, Game 1, Question 3

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### Transcript

Question three. Question three is another local question that adds a condition, and they're asking what must be true? So if the third digit is not a 0, says the condition. Anytime you have an if condition with a split sketch, like we have, you have to check to see which sketch that could take place in, one or both of them.

Here, it could take place in both. In the top scenario, you don't have to make the third digit a 0, you can make it a 3. In the bottom scenario, you don't have to make third digit a 0, you could make it a 1. So that means we're gonna need to do a sketch for each of the scenarios.

So put down two sets of spaces, fill in the non 0 third digits. So 3 in the first option, 1 in the second. That means that the fifth digit, which has to be more than the third digit, in the first case is gonna be a 4. In the second case, it's gonna be a 3. Which leaves a 0 for the fourth digit in both cases.

Each of the sketches is completely determined. So we're looking for what must be true. Answer choice A says that the second digit is a 2. That could be true but doesn't have to be true. In the second scenario, it's a 4. Answer choice B Says the third digit is a 3.

That can be true up top, but it's not true down below. Answer choice C, the fourth digit is a 0. Since that is true, that is our answer, so we don't need to check the other two. But just to explain why they're wrong, answer choice D says that the fifth digit's a 3. It could be, but doesn't have to be because it could be a 1.

Answer choice E says that the fifth digit is a 1. Well, that actually could never be true. It's always either a 4 or a 3.