An oft-repeated challenge on The Challenge
I was watching the finale of America's 5th professional sport, aka MTV's The Challenge: Bloodlines, and was surprised to see the final challenge was a puzzle that I've already seen the show use twice before.
And yes, I realize it might be surprising that someone like me might be watching this show, but in my defense this was season 27, which means I started watching the show when I was very young and it has become somewhat of a tradition to watch. This season wasn't that great, and actually the show hasn't been that great for a while, but what show do you stop watching after 20 seasons? And besides, I have to watch something on my lunch breaks.
Back to the puzzle. This actually isn't the first time I've seen the show reuse a puzzle, they also have reused the puzzle with 10 blocks that need to become five stacks of two. You would think that when there is 250,000 dollars on the line the contestants would realize these puzzles are being reused and memorize the solutions, but if you watch the show you'll know how ridiculous of a proposition that is

^{1}. So in this puzzle there are three rows and three columns, basically a tic-tac-toe grid, and contestants are given the numbers 1-9, and need to place the numbers such that each row, column, and diagonal sum to the same number. And no, this is not Sudoku. This problem may seem difficult and you might be tempted to just start randomly placing numbers in the grid and see what happens, but for a problem-solving savant this is a very basic puzzle. Below I have labeled the positions A-I. A B C D E F G H I The first thing we need to realize is that each position in the grid is not the same. Position E, the center of the grid, will be used in two diagonals, a row, and a column for a total of four sums, while the corner spots will be used in a row, a column, and a diagonal for a total of three sums, and positions B,D,F,H will be used in a row and a column for a total of two sums. With just this information we can determine where the numbers go. The most flexible number needs to go in the middle. But what is the most flexible number in the set 1,2,3,4,5,6,7,8,9? We can use symmetry to arrive at the answer. There is only ONE most flexible number, therefore that number must be unique in some way. Which number is unique? Is it the number 1? It can't be because the number 9 has the same properties as the number 1 (it is the same distance from the average). The same argument can be used for numbers 2 and therefore 8, 3 and therefore 7, 4 and therefore 6. The only number that does not have a partner is the number 5, which is the average of the set, and is the most flexible number. So our solution must have the number 5 in the middle of the grid. A B C D 5 F G H I But where do we go from here? Well the most flexible number needed to go in the middle, where it will be a part of four sums, so the least flexible numbers need to go at positions B,D,F,H. Which numbers are the least flexible? The most extreme numbers are the least flexible, so the numbers 1 and 9. And because of their extreme values we should put them in the same row or column (doesn't matter which). This results in the completion of a row or column, and a sum of 15. So we now know what the sum must be each row and column. A 1 C D 5 F G 9 I How to proceed next is not super obvious. Given how extreme the values of 9 and 1 are, we need to make sure the other row or column they are a part of include the next most extreme values. So the numbers 2 and 8. A 1 8 D 5 F 2 9 I The puzzle is now essentially complete. Filling in the rest of the boxes one by one results in the final solution. A 1 8 D 5 F 2 9 4 A 1 8 D 5 3 2 9 4 A 1 8 7 5 3 2 9 4 6 1 8 7 5 3 2 9 4^{1. One contestant, Sarah, considers herself a professional puzzle solver. But I have doubts...many doubts.↩}