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D32. Tangellipses
Posted: 2025-12-24 16:22:47 Solutions will be accepted through 2025 Jan 2We’ve featured a few Dilemmas from PMP participants about the properties of ellipses. But it turns out that they are a perennial source of interesting questions and problems for the entire mathematical community. For example, six years ago, when the Problem Warden was the Playground editor for the Mathematical Association of America, he wrote down…
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D31. Mono Nonograms
Posted: 2025-12-24 16:13:37 Solutions will be accepted through 2025 Jan 2These problems are based on a type of puzzle called a nonogram: you are given a grid (usually a rectangular portion of a square grid), and each row and column is labeled with a list of numbers that gives the sizes of the blocks of consecutive squares that should be colored black in that row…
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D30. Disambiguated Triangle
Posted: 2025-12-24 15:03:21 Solutions will be accepted through 2025 Jan 2These questions are based on a puzzle that new contributor Stanley Wu-Wei Liu picked up from WeChat and translated from Chinese for us. Your friend tells you that they have placed the six numbers 2, 3, 4, 5, 6, and 7 in the circles in the diagram in the figure to the left so that…
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D29. Geometric-Trigonometric Inequality
Posted: 2025-12-23 16:44:24 Solutions will be accepted through 2025 Jan 2Since no respondents provided a solution to his last problem, Prof. Aliyev is willing to offer one more chance to unravel his mysterious diagrams. In the accompanying figure, nonintersecting circles with radii r < R have common external tangent lines A B and C D , where the named points are the points of tangency.…