STEP 2

START with the top-left 3x3 block: 16 + 13 + 9 = 38. We know that the whole block must add up to 45 — so the only cell that is not contained by those cages must have the number (45-38) = 7. There are only two cells in that cage and the total is 9 so put a (9-7)= 2 in the outlying cell.

Now repeat this trick wherever you can see it. There’s a 6 in the middle-left box, accompanied by a 1 for that cage. And a 5 in the top-right box, with a 6 below it. Also, in the bottom-right block, 14+10+18=42. As 45-42=3, we know that the top cell of the cage of 8 must be a 5. By the same process, we can place a 5 in the bottom-left box.