Monthly Archives: October 2016

Pip Total as Prime Number

A pair of six-sided dice is tossed. What is the probability that the pip total is a prime number? Source: NCTM Mathematics Teacher, January 2006 Solution Number of possible outcomes Desirable outcomes Number of desirable outcomes Probability that the pip … Continue reading

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Black Hair Red Hair

A man and a woman were the only two people walking along a beach. “I’m a man,” said the one with black hair. “I’m a woman,” said the one with red hair. At least one of them was lying. What … Continue reading

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Numbers Greater Than 5,000,000

Using all the digits and , how many distinct integers greater than can be formed? Source: NCTM Mathematics Teacher, January 2006 Solution The first digit must be a or a . Case 1: _ _ _ _ _ _ Since … Continue reading

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Convex Polygon

What is the maximum number of acute angles that any convex polygon can have? Source: NCTM Mathematics Teacher, January 2006 Solution The Polygon Exterior Angles Theorem states that the sum of the measures of the exterior angles of a convex … Continue reading

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Arithmetic Sequence

Find the values of the digits , and in the four terms of the following arithmetic sequence: . Source: NCTM Mathematics Teacher, January 2006 Solution The four terms can be expressed as The terms of an arithmetic sequence are increasing … Continue reading

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Lattice Points

A point with integral coordinates is called a lattice point. For example, is a lattice point, whereas is not. How many lattice points lie on the graph of ? Source: NCTM Mathematics Teacher, January 2006 Solution The graph of is … Continue reading

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