fall-2017-final

Solutions to Spring 2017 HEXA Challenge Problems

previous month's work, and from that amount, at the end of the month, he has $1,000 left. When should the collection agency next meet with him to settle his debt?

SOLUTION: The problem is purposely ambiguous. Several simplifying assumptions have to be made in order to solve it. The information on the monthly pay is not provided. According to the U.S. Census Bureau (https:// www.census.gov/topics/income-poverty/income.html), income for a single person is about $3,000. We are also making an assumption that he does not spend during the month he is working but he gets paid. Therefore:

Months

Total Funds

The debt collector should be able to collect money at the end of the fifth month.

1

$3,000

2

$3,000 + $1,000

3 4

$4,000 + $3,000 $7,000 + $1,000

5

$8,000 + $3,000

August Challenge: The shadows of a three-dimensional object cast on three planes perpendicular to each other create a circle, a square, and an equilateral triangle. What is the shape?

SOLUTION: Imagine a cylinder, whose base diameter and height are equal to each other. AB and CD are mutually perpendicular base diameters lying respectively in the upper and lower bases of the cylinder. The cylin- der has been cut so that the 'shoulders' could be taken off (Figure 1). Let's see what remains:

Figure 1. The cylinder with the ‘shoulder’ cut lines.

Virginia Mathematics Teacher vol. 44, no. 1

38