Monthly Archives: September 2016

Perfect Squares and Perfect Cubes

List all integers less than that are both perfect squares and perfect cubes. Source: NCTM Mathematics Teacher, January 2006 Solution is a perfect square but not a perfect cube. On the other hand, is a perfect cube but not a … Continue reading

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Ten Different Digits

What is the probability that a number chosen at random from the range to inclusive will contain ten different digits? Round your answer to the nearest millionth. Source: NCTM Mathematics Teacher, January 2006 Solution We divide the large range into … Continue reading

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Corners of a Cube

All corners were sliced off a cube whose volume was cubic centimeters. Triangular faces are located where the cube’s vertices were. Each triangle is equilateral with -centimeter sides. Determine the total numbers of edges on the new solid. Source: NCTM … Continue reading

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Mean of Numbers

The mean of a set of numbers is . If one number is increased by , the mean increases to . How many numbers are in the set? Source: NCTM Mathematics Teacher, January 2006 Solution The formula for the mean … Continue reading

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Four Numbers

The numbers , and are such that the sum of any one of them and the product of the other three is equal to . If , and , find . Source: NCTM Mathematic Teacher, January 2006 Solution There are … Continue reading

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Changing Seats

Thirty-five students are seated in five rows and seven columns. Is it possible for the students to change seats if every student must move exactly one seat to the left, right, front or back? Source: NCTM Mathematics Teacher, January 2006 … Continue reading

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