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June 2007, Game 1, Question 1


This question is a local question. It's asking us about what must be true? So we're going to begin by creating a new sketch, the spaces 1 through 5, and we add the condition to it. So the condition here from question 1, the condition here from question 1 is the last digit has to be a 1.

So fill that in. Now, so in a game where you have two possibilities, as we do, you have to consider which one the if can work in. If we're using the number 1 in the fifth slot, that means that we have to be in the second of our scenarios, the one where 2 and 4 start it out. And because of the fourth rule, which says that the fifth slot has to be more than the third, that means that the third slot can't be any number bigger than 1.

We only have one number less than 1 left, that's 0. And that means that the only number left at all for the fourth slot is going to be 3. So that sketch is completely determined. All we have to do is look to the answer choices. We're looking for what must be true.

Answer choice A says the first digit is a 2, and that is something that must be true. And because it must be true, there can't be another answer that's right. So that is our answer. So we move on to question 3.

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