GeekDad Puzzle of the Week Solution – Roundtable Elimination

The puzzle, as previously presented:

Twelve people sit at a table in a conference room, knowing that eleven of them will be let go by the end of the meeting. Our hero, who would like to stay gainfully employed, knows that the CEO will soon enter the room. At that time, starting with the person closest to the door (in the “12 o’clock” position of the table), the CEO will start circling the table, stating:

“Eeny meeny miney moe.
Catch an employee by the toe.
If he flinches, let him go.
Eeny meeny miney MOE.”

Each verse of the macabre rhyme takes four beats, and on each beat, the CEO passes one person in a chair. Assume for purposes of this puzzle that he is dextrous enough to circle the table in such a way that he moves through four people each verse, completely independent of where they are sitting. Also note that he always moves in a clockwise manner.

Upon completing the rhyme, the CEO then presents a pink slip to the person in the occupied chair at which he stopped. Identifying the first person to be let go is straightforward. However, picking the seat that will get to stay after the other 11 are eliminated is not as simple!

Completing this week’s puzzle took a steady hand, a sharp pencil, and the ability to reliably count to 16. Of course, the first three times I attempted to solve this puzzle while creating it, I got three different answers!

It appears that there was some dissent among the responses around the chair on which the first beat (the initial “eeny”) fell. Was it the 12 o’clock position or the 1 o’clock position? For purposes of entering responses in the random drawing, responses indicative of starting on either were accepted. For my solutions below, I started on the top most position — and it contained the highest value (12, 8, or 16.)

Starting with table of size 12, and putting 12 as the top position (like a standard clock), the various hours of day are “knocked out” in the following order:
3, 8, 2, 11, 10, 1, 7, 9, 6, 12, and 5, leaving the 4 o’clock as the last spot standing.

With a table of size 8, having 8 at the top, the seats are “knocked out” in the following order:
7, 1, 5, 6, 4, 8, and 3, leaving 2 as the last spot standing.

With a table of size 16, having 16 at the top, the seats are “knocked out” in the following order:
15,16,2,5,9,14,8,4,3,7,13,1,12,6, and 11, leaving 10 as the last spot standing.

Congratulations to Keith Griffith, the winner of this week’s \$50 ThinkGeek gift certificate.  Not only did Keith provide a correct response for the 12-seat table, but also stated that “unless the boss is in the middle of the table on a Sit’n’Spin, I don’t see how he’s making the rounds and keeping the beat on time.”

Thanks to everyone that posted a solution. I hope that you enjoyed the puzzle!