The game that inspired my question was a fun activity for both children and adults during the hey-day of carousel/merry-go-round rides, 1880-1930.  Rings were made of nickel and brass, and “going for the brass ring” was an often-used expression.  There are still a few carousels/merry-go-rounds in the United States that feature the Ring Game, but I would have to close my eyes and listen to the music to recapture the experience.

These are the essential features of the amusement park ride I call “The Original Carousel Ring Game.”  Rings displayed by the merry-go-round I rode were so special to me that I called them Silver and Gold.

• You are one of the riders on a carousel/merry-go-round.
• Alongside the carousel is a downward sloping ring dispenser.
• The dispenser holds an unknown number of Silver Rings followed by a single Gold Ring.
• The carousel/merry-go-round rotates in a counter-clockwise direction.
• Each rider takes the available ring with his/her right hand when passing the dispenser; Southpaws are disadvantaged by counter-clockwise rotational direction.
• The rider taking the last Silver Ring makes the Gold Ring available to his/her successor.
• The rider taking the Gold Ring wins a free ride.

Provided each rider takes a ring on every turn at the dispenser, “The Original Carousel Ring Game” is formally equivalent to “Eenie, Meenie, Miney, Moe”; the Chant-caller assigns words just like the dispenser presents rings.  The playing position of the rider taking the Gold Ring is determined by the same division operation as the child associated with the last chant word.  These two are the same take-away game.

This is also the case for “Fortune-Telling With Daisy Petals”, even though you are the sole “player”; the daisy dispenses petals instead of rings.

“The Original Carousel Ring Game” is also twin to the “parlor trick” described in Blog #2, “Clock Arithmetic”; there, the remainder after simple division identified the correct day of the week or month of the year. 

Blog posts #2, #3 and #4 use no math beyond 5^th grade.  But suppose you are a parent or older sibling to a youngster who has not yet encountered division?  What would be a good “lesson plan” for demonstrating the common ground underlying these four “Take-Away” games? 

Here is my suggestion:  (1) explain simple division as “grouping”; (2) make concepts concrete by creating a simple apparatus to play “The Original Carousel Ring Game”. Then, demonstrate how division/grouping can be used to predict which rider gets the Gold Ring in “The Original Carousel Ring Game. 

To complete the lesson plan, refer back to the “days of the week” or “months of the year” calculation in Blog post #2, “Clock Arithmetic”.  Show that the division operation used in “The Original Carousel Ring Game”, is also used in Blog post #2.  The Takeaway from Take-Away Games is that elementary arithmetic often reveals the underlying similarity between apparently different phenomena.

Questions for parents or older siblings: 

What is the winning playing position on a 4-position carousel if the number of rings is divisible by 4?

What is the winning position if the youngster chooses a ring dispenser smaller than the number of carousel playing positions?

Ask if the youngster can determine the winning rotation number from the number of ring “groups” by using multiplication.  Hint:  count the number of rings taken during completed rotations by repeated additions.

What happens if one of the Takers misses a ring?  See Blog post #6.

Now try the lesson plan in my post 5.1 which provide an enhancement activity for younger students.