Number 27, Patricia wants to write the numbers from one to nine into the squares in the diagram, with one number in each square. She wants the sum of the numbers in any two adjacent squares to be equal to the number shown on the line joining these squares. What is the sum of the numbers she writes in the shaded row? Pause if you want to try and solve it. Okay, so there's actually a trick for this one that lets us figure it out really quickly. Think about the number one, right? We have to write one in one of these squares. And if we have a line joining it to another square, whatever we put in this other square, the sum of those numbers of one and that number will be less than or equal to ten. Because even if we choose the largest possible number, nine, the sum of one and nine is ten. What that means is that any square that has one in it will only have lines coming out of it that have a number that is less than or equal to ten, right? All of these lines have to be less than or equal to ten. And there's actually only one square that fits its description, right? Over here, 11 and 13 are both bigger than 10. Over here, 11 and 13 bigger than 10, right? Every single square that we choose, it has at least one number that's bigger than 10. There's only one square that doesn't. It's this one over here. And so that means that this square has to be one. That's the only place where we can put one. And so now that means that if this one is one and this is ten over here, right? This square has to be nine because nine plus one is ten. And then if this is 13, that means this has to be four because nine plus four is 13, and four plus five is equal to nine. So that means that the squares in the middle actually have to be five, four, and nine. And so what's the sum of those squares? Well, five plus four is nine, and nine plus nine is 18. So the correct answer is 18, which is option C.

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