Problem 9 · 2020 Math Kangaroo
Easy
Logic & Word Problems
Arithmetic & Operations
magic-squaresum-constraintwork-backward
Juca wrote a whole number greater than zero in each box of the 3×3 board shown, so that the sums of the numbers in each row and in each column are equal. The only thing Juca remembers is that no number is used three times. What number is written in the center box?
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Answer: C — 4
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Hint 1 of 2
All three rows and columns share the same total; the top row 1 + 2 + 6 gives that total.
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Hint 2 of 2
Fill the grid from the common sum of 9, using that no value may appear three times.
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Approach: use the common row/column sum
- Each row and column sums to 1 + 2 + 6 = 9.
- The left column 1 + 3 + ? = 9 forces the bottom-left to be 5.
- Filling in keeps the sums at 9; the center value can be 4 (center 5 would repeat a number three times, which is forbidden).
- So the center is 4, choice C.
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