fall-2017-final

Please be sure to state your assumptions as you solve each problem. Answers to the Fall 2017 Hexa Challenge Problems

Contest Alert!

Virginia Mathematics Teacher is conducting a contest for educators and students who can solve the great- est number of problems correctly by 02/28/2018. The winner will receive a prize and will be featured in the next issue of the VMT. Send your solu-

will be featured in the Spring 2018 Issue of Virginia Mathematics Teacher.

tions to vmt@radford.edu with the email subject line: Hexa Challenge

January Challenge: Find all the integer pairs (X; Y) that satisfy the equation X 2 ‒ 5XY + 6Y² = 11.

February Challenge: You bought a duck from a market place. Your duck lays 10 eggs, and then all the 10 eggs safely hatch. After these eggs hatch you eat the duck for dinner. The newly hatched ducklings that are drakes (male ducklings) get eaten. However, you allow the female ducklings to mature and have 10 eggs each. Once they lay ten eggs, you eat the duck. The same principle continues: male ducklings become eaten as early as possible, but you allow female ducklings to mature and have 10 eggs, only then you eat the female ducks. Unfortunately, one day only drakes (male ducklings) hatch from all eggs. You eat them all. You have counted that all together you have eaten exactly 1000 drakes. How many ducks (female) have you eaten?

March Challenge: There is a coordinate system with the origin O, where OA = 5 units, OB = 6 units, and OC = 7 units. Estimate the area of the triangle ABC.

Virginia Mathematics Teacher vol. 44, no. 1

31