Problem number 18. Stephen wants to pick two numbers from the board and add them together. How many different results could Stephen get? 5, 6, 7, 8, or 10? We could solve this problem by adding each pair of numbers together. For example, picking 1 plus 2, 1 plus 3, 1 plus 4, 1 plus 5, and 2 plus 3, 2 plus 4, and so on. But I want us to actually think about what the smallest result and the largest result are when we add two of these numbers. The smallest result comes from adding the two smallest numbers, 1 and 2, that is 3. The largest result is from adding the two largest numbers, 4 plus 5, which is 9. All the other results we could get are between these two numbers, and they are whole numbers. So we could have 3, 4, 5, 6, 7, 8, and 9. And that would be seven different results. What we need to do now is check whether we can get these other results. We can get 4 by adding 3 and 1. We can get 5 by adding, for example, 2 and 3. For the 6, we could add 4 and 2. For 7, we could add 2 and 5. And for 8, we would add 5 and 3. So we can get all these results, and there are seven of them. So the answer is C, 7. Stephen can get seven different results.

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