# Monthly Archives: March 2018

## Smaller Factor

Given a three-digit number, interchange the units digit and the hundreds digit. The product of the original number and the new number is . What is the smaller three-digit factor? Source: NCTM Mathematics Teacher, February 2008 Solution Since the product … Continue reading

## Non-Congruent Triangles

Among the triangles of the previous problem (repeated below), how many distinct (non-congruent) triangles exist? Previous Problem: How many distinct triangles can be constructed by choosing three vertices from among the corners of a unit cube? Source: NCTM Mathematics Teacher, … Continue reading

## Distinct Triangles

How many distinct triangles can be constructed by choosing three vertices from among the corners of a unit cube? Source: NCTM Mathematics Teacher, February 2008 Solution We construct four triangles from three corners of a face for a total of … Continue reading

## Measure of Angle Z

Find the measure of the angle in the diagram here, given that the two horizontal segments are parallel. Source: NCTM Mathematics Teacher, February 2008 Solution Complete a seven-sided concave polygon by drawing a perpendicular line to the two parallel lines … Continue reading

## Square of 111,111,111

Find the exact value of . Source: NCTM Mathematics Teacher, February 2008 Solution Answer: Alternative solution Multiply the numbers manually using the old-fashioned multiplication algorithm. It should be straightforward because there is no “carry”.

## Two Even Digits

The number is a four-digit number having two zeros and two even digits that are not zeros. How many four-digit numbers besides can also be described this way? Source: NCTM Mathematics Teacher, February 2008 Solution First, choose a way to … Continue reading

## Product of Factorials

Solve for if . Source: NCTM Mathematics Teacher, February 2008 Solution Answer:

## Four Congruent Rectangles

Four congruent rectangles are arranged as shown in the figure to form a large rectangle. The area of the large rectangle is . What is the area of a square that has the same perimeter as the large rectangle? Source: … Continue reading

## Sum of Six Angles

Find the value in degrees of the sum of the six angles indicated in the diagram. Source: NCTM Mathematics Teacher, February 2008 Solution The three triangles contain nine angles, three of which form a straight angle. Hence, the sum of … Continue reading

## The Second Number

The sum of three numbers is . The first number is of the second, and the second is of the third. What is the second number? Source: NCTM Mathematics Teacher, February 2008 Solution Let be the first, second, and third … Continue reading