Can you solve “Challenger” puzzles?

Question

They appear in daily newspapers (including the San Francisco Chronicle). Here's an example.http://www.10zenmonkeys.com/2021/12/08/when-a-newspaper-publishes-an-unsolvable-puzzle/But there's dozens of solutions. I understand a computer could eventually calculate them all. My question is how everyday newspaper readers can solve them with just a pen and paper.The totals for the rows still leave many, many possibilities. Is the idea to just start trying numbers, and then backtracking again and again, until eventually you stumble on a winning path?

gus_massa · Accepted Answer

I never played this, so it's difficult to know the best tricks, but from other similar games, the idea is to discover as much as possible and when you get stuck, use brute force.
In this case I couldn't discover any number, but the row with 32 looks very promising, because 32 is almost 36 that is the maximum. So each square in that row must be 6, 7, 8 or 9.
Also, from the diagonal you can know the sum of the 2x2 square at the top right, and then calculate the sum of the other 2x2 square in the other corners. In particular the sum of the two missing squares in the bottom right is 11.
My totally unsupported guess is to try all the possibilities of the square in the 3rd row, rightmost column (with a 32 in the sum of the row and a 30 in the sum of the column).
If it's a 6, all the other in the row must be 9, so you advance a lot.
If it's a 9, then the other missing square in the bottom right is 2, that is very low and the third column and bottom row look interesting.
With 7 and 8 there may be more work, until you get something interesting.
My preferred method when I'm going to branch like here in 6, 7, 8 and 9, is to make four copies of the board with the current information. Some people just write the guess, but later it's difficult to erase all the deductions from the guess and try another guess. When you are guessing don't be lazy and make a full copy of the board for each of the possible guess.
As you may realize, this created a lot of copies of the board, so the trick is to guess as few times as possible and try to pick a square with very few choices. In this case it's 4 that is too much for my preferences, but I couldn't find anything better. Also I prefer to try first the choices in the extreme that looks less promising, so I can find that it's impossible soon and cross out that copy of the board.
It's essentially backtracking and proof by absurd, implemented in many sheets of paper.