vmt-award-2024_48-1-_red

Challenge 4:

A sequence is defined recursively with

and

for

What is

?

Challenge 5:

Give the decimal representation for the set of positive integers that are four - digit numbers with no leading zeros when expressed in both base 6 and base 8.

Challenge 6: Starting with a regular hexagon with edge length 1, form a smaller hexagon inside it by connecting the midpoints of the six edges, and then repeat this process. The perimeter of the first hexagon is 6. How many times must this process be repeated before the perimeter becomes a rational number again?

Please be sure to state your assumptions as you solve each problem. Answers to the 48(1) Hexa Challenge Problems will be featured in the 48(2) issue of Virginia Mathematics Teacher.

Contest Alert!

Virginia Mathematics Teacher is conducting a contest for educators and students who can solve the great est number of problems correctly by December 10, 2023. The winner will receive a prize and will be featured in the next issue of the VMT. Send your solutions to vmt@radford.edu with the email subject line: Hexa Challenge

Virginia Mathematics Teacher vol. 48, no. 1

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