Problem number 23, a spiral of consecutive numbers is created as shown starting with one. When the pattern of the spiral is continued, in which arrangement will the numbers 625, 626, and 627 appear? Alright, so first, you always want to expand the table a bit more just to see what the pattern is, and then look at like, okay, where does 625 fit in? Also, we're going to take note of the fact that 625 is equal to 25 squared, or 5 to the power of 4. We don't know if that's useful, but just good to keep in mind. So if I expand the table, I notice that I have 1 through 9 through 25 through 49. And the highest number in any given square is always in the corner. So 49, 25, 9, 1. So 1 squared, 3 squared, 5 squared, 7 squared. Hey, wait a second, it's just the square of all the numbers is always in the top left corner. It's the square of all the odd numbers. So the square of all the odd numbers is always in the top left corner. Well, 25 squared, 25 is odd, that's going to be in the top left corner. And if we move on, we can notice that pattern. So if we have 25 squared, right after 9, we go up 1 to find the next number, and then to the right. For 25, we go up 1, and then to the right. For 49, we would do the same thing. And for 625, the pattern would keep on going, and we would keep on going up 1. And we would get that the correct answer is B.

spiral pattern

consecutive numbers

square of odd number

top-left corner

sequence arrangement