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D4. Four Operations Revisited
Posted: 2022 Jan 30One of the great things about mathematics is that it’s always possible to look again at familiar things and discover something new. Sometimes this can happen when you combine well-known things in a new way. For example, you’re probably familiar with the four basic operations of addition, subtraction, multiplication, and division. And you may have…
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D3. Zero Sum Game
Posted: 2022 Jan 29Is it possible to number the edges of a cube using each of the numbers -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, and 6 once, so that for every vertex, the sum of the numbers on the edges that meet there is zero? (See figure 1 for a diagram of the…
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D2. Find Yourselves
Posted: 2022 Jan 28In this classic dilemma, the director of a prison offers 100 people slated to be locked up one last chance at freedom. The individuals have been assigned different numbers from 1 to 100, and the director sets up a room containing 100 boxes. Each number from 1 to 100 has been put on a slip…
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D1. Continuing Irrationality
Posted: 2022 Jan 27One interesting thing about continued fractions is that every infinite continued fraction represents an irrational number. But in our first dilemma, we ask what happens when you have an infinite sequence of finite continued fractions with more and more terms. Recall that the binomial coefficient ( a b ) has the formula a ! b…