# Monthly Archives: January 2016

## Walk to School

Jaisi runs twice as fast as she walks. When going to school one day she walks for twice the time she runs and takes minutes to complete the trip. On her way home after school, she runs for twice the … Continue reading

## Shorthand Notation

We can devise a shorthand notation for large numbers by letting stand for the occurrences of consecutive s where is a positive integer and is a fixed digit between and . So, would denote the number . Find the ordered … Continue reading

## Tossing Die

Amy, Ben, and Charlie repeatedly take turns tossing a fair die in the given order . What is the probability that Charlie will be the first one to toss a ? Source: NCTM Mathematics Teacher, December 2005 SOLUTION The possible … Continue reading

## Boring Book

After finishing a very boring book, Fred notices that the page numbers contained exactly zeros and exactly ones. The book started with page . How many pages were in the book? Source: NCTM Mathematics Teacher, December 2005 SOLUTION We arrange … Continue reading

## Circles Within Square

The two circles in the figure are congruent and have their centers on the line . They are tangent to each other and to the square . The radius of the circles is . Calculate the area of the square … Continue reading

## Sum of Integers

The sum of three positive integers is . Taken in pairs, their differences are , and . Find all possibilities for the three numbers. Source: NCTM Teacher, December 2005 SOLUTION Suppose the three positive integers are such that . The … Continue reading

## Measure of Angle

, and are vertices of a cube, as shown. Find the measure of . Source: NCTM Mathematics Teacher, December 2005 SOLUTION Triangle is equilateral because its three sides are diagonals of a square. The measure of equals . Answer:

## Inscribed Squares

Two squares are inscribed in a semicircle, as shown. The area of the smaller square is . What is the area of the larger square? Source: NCTM Mathematics Teacher, December 2005 SOLUTION is the center of the circle and also … Continue reading