Paper
The Playground
Published Dec 28, 2018 · Glen Whitney
Math Horizons
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Abstract
Tough Pill to Swallow (P382). Each day, Professor Kibacha takes a half a pill as follows: she dumps one item out of the bottle (uniformly randomly selected). If it’s a half pill, she swallows it; otherwise, she breaks it, takes half, and puts the other half back. One day, a whole pill shakes out but drops down the drain. After counting the whole and half pills remaining, the professor thinks, “Hmm, losing that pill did not change the expected number of half pills in the bottle when I end up breaking the last whole pill.” What is the difference between the number of whole pills and half pills left in the bottle? Triangular Triad (P383). This problem was submitted by Arsalan Wares from Valdosta State University. Point K is on side BC of triangle ABC and M and N are the midpoints of the sides adjacent to A, as shown in figure 1. Point P is the intersection of AK and MN, and Q is the intersection of AK with median CM. If triangles APN and MPQ both have area 5 units, what is the area of triangle CKQ?
Losing a whole pill does not change the expected number of half pills in the bottle when breaking the last whole pill.
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