benchmarks.wiki / Public workspace
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Omni-MATH / Draw a rectangle. Connect the midpoints of the opposite sides to get 4 congruent…
Problem
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problem
Draw a rectangle. Connect the midpoints of the opposite sides to get 4 congruent rectangles. Connect the midpoints of the lower right rectangle for a total of 7 rectangles. Repeat this process infinitely. Let be the minimum number of colors we can assign to the rectangles so that no two rectangles sharing an edge have the same color and be the minimum number of colors we can assign to the rectangles so that no two rectangles sharing a corner have the same color. Find the ordered pair .
Plain-text mathematical notation (without MathML)
Draw a rectangle. Connect the midpoints of the opposite sides to get 4 congruent rectangles. Connect the midpoints of the lower right rectangle for a total of 7 rectangles. Repeat this process infinitely. Let n be the minimum number of colors we can assign to the rectangles so that no two rectangles sharing an edge have the same color and m be the minimum number of colors we can assign to the rectangles so that no two rectangles sharing a corner have the same color. Find the ordered pair (n,m).
Original LaTeX notation
Draw a rectangle. Connect the midpoints of the opposite sides to get 4 congruent rectangles. Connect the midpoints of the lower right rectangle for a total of 7 rectangles. Repeat this process infinitely. Let $n$ be the minimum number of colors we can assign to the rectangles so that no two rectangles sharing an edge have the same color and $m$ be the minimum number of colors we can assign to the rectangles so that no two rectangles sharing a corner have the same color. Find the ordered pair $(n, m)$.
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Source and history
- task_id
5a442c21-aee0-57a7-8df6-90766e7ab161- task_key
test--5a442c21-aee0-57a7-8df6-90766e7ab161- task_revision_id
- 1
- config / split
- / test
initial import