Problem number 3. Sandra rolls 3 dice and gets a total of 8. Each of the 3 dice shows a different number of dots. Which number of dots could Sandra not have rolled on any of her dice? To solve this problem, let's think about the largest value that she could have rolled on the dice. In particular, let's think about 6. If 6 was used, then we need the 2 remaining dice to have a sum of 2. But that's not possible, because 1 plus 1 equals 2, and that's the only way you can get to 2, but these numbers are not different, and the problem says that each of the 3 dice shows a different number of dots. This means that the answer is E, 6. To show that this is the only possible answer, we can try other combinations that add up to 8. 1 plus 2 plus 5 equals 8, and 1 plus 3 plus 4 equals 8, so Sandra could have rolled a 2, 3, 4, or 5, but we've proven that it's definitely impossible for Sandra to roll a 6, so the answer is E, 6.

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