Problem 19 · 2024 Math Kangaroo
Hard
Logic & Word Problems
magic-squaresum-constraint
Daniel forms a 4×4-square out of the three pieces shown on the right and another piece. The sum of the four numbers in each row and in each column is the same. What does the fourth piece look like?
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Answer: A
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Hint 1 of 3
Place the three given pieces in the 4×4 grid and look at any row or column that is already complete to read off the common line sum.
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Hint 2 of 3
Once you know the target sum, each empty cell is forced: it must make its row and its column reach that total.
Still stuck? Show hint 3 →
Hint 3 of 3
The fourth piece must fit the leftover three cells with exactly the values those cells require.
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Approach: fit the three pieces, find the common line sum, then force the empty cells
- Slot the three given strips into the 4×4 grid; a row or column that is already full reveals the common sum every line must reach.
- Each remaining empty cell is then forced, since its value must complete both its row and its column to that sum.
- The three forced values, in the shape of the leftover cells, read 1, 1, 3.
- So the fourth piece is (A).
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