# Monthly Archives: March 2014

## Nested Square Roots

Without the aid of a calculator or any other computing device, determine the value of the infinite expression Source: NCTM Mathematics Teacher 2008 SOLUTION Let By substitution Squaring both sides and is an extraneous solution because the expression cannot be … Continue reading

## Sum of Powers of Five

Compute the units digit of . Source: NCTM Mathematics Teacher 2008 SOLUTION 1 The units digits of follows the following pattern. If , the units digits of the sum are . For example, , units digit = , units digit … Continue reading

## Handshakes

A group of high school students, girls and boys, is randomly divided into two rows of students each. Each student in one row is directly opposite a student in the other row, and all the opposite pairs of students shake … Continue reading

## Fives and Eights

Find the greatest positive integer that cannot be expressed as a multiple of , as a multiple of , or as a sum of a multiple of and a multiple of . Source: mathcontest.olemiss.edu 3/24/2014 SOLUTION What kind of numbers satisfy the … Continue reading

## Square Lot

Al and Curt live at opposite corners of a square lot; Beth and Dawn live at the other two corners. They all carry water from a spring located within the lot. The spring is feet from Al, feet from Beth, … Continue reading

## Chessboard

A chessboard of size , using alternating black and white squares, is displayed on a computer screen. One can reverse the color in a selected rectangular subarray of the squares by pressing a mouse-button reverse key. Find the minimum number … Continue reading

## Six-digit Numbers

If all the six-digit numbers formed by using the digits , and , without repetition, are listed from least to greatest, which number will be in the list? Source: NCTM Math Teacher 2008 SOLUTION There are six-digit numbers. We examine … Continue reading

## ABC Triples

, and are real numbers. How many triples exist such that , and ? Source: mathcontest.olemiss.edu 3/3/2014 SOLUTION Divide both sides by assuming Divide both sides by assuming Consider a real number The triples are 1) 2) 3) 4) 5) … Continue reading

## Bicycle Tire

A -inch (diameter) bicycle tire is being calibrated with a speedometer. Approximately how many revolutions of the wheel are equal to mile? Source: NCTM Math Teacher 2008 SOLUTION Circumference of tire where is the diameter. Length of revolution = in. … Continue reading

## Right Angle

If the graphs of the equations and intersect at right angles, find the value of . Source: NCTM Math Teacher 2008 SOLUTION If the two graphs intersect at right angle, their slopes are negative reciprocal of each other Cross multiply … Continue reading