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D24. Sliding Ratios
Posted: 2024-09-30 23:48:51 Solutions will be accepted through 2025 Jul 15As shown in Figure 4, A B C is a triangle. Points F and E lie on side A B , with F closer to B . Point D lies on side A C . Point G is the intersection of segments B D and C E , and H is the intersection of ray…
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D23. Factor Network
Posted: 2024-09-30 15:39:23You want to label the vertices (corners) of a regular octahedron (see Figure 3) with whole numbers bigger than one so that the labels of two vertices have a common factor (bigger than one) if and only if they are adjacent on the octahedron (connected by an edge). Is it possible? If so, what is…
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D22. Fill the Jar
Posted: 2024-09-10 15:13:36You are making sugar cookies from a batch of dough in the following way: You take your dough and roll it into a perfect square of just the right thickness (you are a very precise baker). Then you cut out 1-inch radius, perfectly circular, cookies arranged in a square grid so that the cookies are…
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D21. Light Chase
Posted: 2024-09-10 14:00:15You have a puzzle toy which consists of a ring of lit buttons, each of which can glow red, yellow, or (bluish-)green, as illustrated in Figure 1. When you push a button, its color cycles in the order red → green → yellow → red. The catch is, the lights two positions away in each…