benchmarks.wiki / Public workspace
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Omni-MATH / Nine distinct positive integers summing to 74 are put into a 3×3 grid. Simultaneously, the number in each cell is replaced with the sum of the numbers in its adjacent cells. (Two c…
Problem
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problem
Nine distinct positive integers summing to 74 are put into a grid. Simultaneously, the number in each cell is replaced with the sum of the numbers in its adjacent cells. (Two cells are adjacent if they share an edge.) After this, exactly four of the numbers in the grid are 23. Determine, with proof, all possible numbers that could have been originally in the center of the grid.
Plain-text mathematical notation (without MathML)
Nine distinct positive integers summing to 74 are put into a 3×3 grid. Simultaneously, the number in each cell is replaced with the sum of the numbers in its adjacent cells. (Two cells are adjacent if they share an edge.) After this, exactly four of the numbers in the grid are 23. Determine, with proof, all possible numbers that could have been originally in the center of the grid.
Original LaTeX notation
Nine distinct positive integers summing to 74 are put into a $3 \times 3$ grid. Simultaneously, the number in each cell is replaced with the sum of the numbers in its adjacent cells. (Two cells are adjacent if they share an edge.) After this, exactly four of the numbers in the grid are 23. Determine, with proof, all possible numbers that could have been originally in the center of the grid.
Discussion
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Source and history
- task_id
16e40428-6c36-5f9e-b09e-c9a8a3629abb- task_key
test--16e40428-6c36-5f9e-b09e-c9a8a3629abb- task_revision_id
- 1
- config / split
- / test
initial import