Strike off any digit from each number in seven rows (need not be at same…

This is a digit-deletion ("digit-striking") number puzzle: from every multi-digit number in the working, exactly one digit is struck out (the remaining digits keep their original left-to-right order); the digit struck does not have to be in the same position for every number. The same arithmetic operation (addition or subtraction) applied to the shorter numbers must still hold true, and each reduced result must also match the corresponding digit struck from the original, longer result one stage down.

1. Strike the '2' (hundreds place) from 1234 to get 134, and the '4' (hundreds place) from 3455 to get 355.

2. Add the reduced numbers: 134 + 355 = 489.

3. Check consistency: striking the '6' (hundreds place) from the original result 4689 also gives 489, confirming this reduced sum is consistent with the full four-digit working.

4. For the subtraction, strike the '3' (hundreds place) from 2345 to get 245.

5. Subtract: 489 - 245 = 244.

6. Check consistency: striking the '3' (hundreds place) from the original difference 2344 also gives 244.

7. For the final addition, strike the last '4' (ones place) from 1254 to get 125.

8. Add: 244 + 125 = 369.

9. Check consistency: striking the last digit '8' (ones place) from the original sum 3698 also gives 369.

At this final stage, striking a different single digit from 1254 -- say the hundreds digit '2' instead of the ones digit '4' -- would give 244 + 154 = 398, which also matches a valid strike (the hundreds digit) of the printed result 3698; another single-digit strike gives 244 + 124 = 368. So more than one internally consistent three-digit total exists at this stage. Of the four numbers offered as options, however, only 369 appears -- 398 and 368 are not offered -- which fixes 369 as the result this question is built around.

Every reduced three-digit result in the chosen chain matches the corresponding digit-struck form of the original four-digit result, so 134 + 355 = 489, 489 - 245 = 244, 244 + 125 = 369 is fully self-consistent. The same digit-striking process continues on to a two-digit chain and then a one-digit chain, following the identical logic.

So the three-digit number obtained at this stage is 369.