Problem 11 · 2022 Math Kangaroo
Medium
Logic & Word Problems
magic-squaresum-constraint
Mosif has filled a table with numbers (see diagram). When he adds the numbers in each row and in each column, the result should always be the same, but he has made a mistake. To make every total the same he has to change one single number. Which number does Mosif have to change?
| 9 | 1 | 5 |
| 3 | 7 | 6 |
| 4 | 7 | 4 |
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Answer: B — 3
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Hint 1 of 2
Work out every row total and every column total and see which one is the odd one out.
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Hint 2 of 2
The number to change sits where the wrong row crosses the wrong column.
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Approach: find the row and column that are off
- The row sums are 15, 16, 15 and the column sums are 16, 15, 15, so the target is 15.
- One row is 1 too big and one column is 1 too big.
- The cell in both that row and that column is the 3; lowering it to 2 fixes both.
- So Mosif must change the 3.
Mark:
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