Never guess a cell — force it.

Scan all six equations (two rows, plus the three columns whose results sit in the bottom row) and start with the line holding the most givens. A line with two of three cells known forces the third — no choices, just arithmetic.

Every cell you fill upgrades some crossing line from one given to two. Follow the chain: fill a cell, immediately check the row AND column it belongs to — one of them is usually now forced. A typical grid falls in four or five forced steps without ever “trying” a number.

The classic traps are subtraction lines. In a − b = c, a missing a is c + b (add!), while a missing b is a − c. Say the role of the blank to yourself — “it’s the thing being subtracted” — before computing. Most wrong grids are one flipped sign, not bad arithmetic.

You never need to re-check all six equations. The last cell you fill sits on one row and one column — if both of those hold, the grid is consistent, because every other line was already forced true. Submit and move on.

Early grids are all-addition with many givens — those are pure typing speed, bank them fast. When subtraction appears and givens thin out, slow down half a beat on sign traps: a miss costs the retry AND the re-read, which is worth more than the half-second you saved.