by Dave Youngs
This month we take a break from puzzles, to take a look at a holiday problem solving activity.
This activity is based on the traditional English song The Twelve Days of Christmas. According to The New Oxford Book of Carols, this song has its origin in a traditional forfeits game which was played on Twelfth Night, the eve of Epiphany. In games of this type, each player would have to recall the objects recited by previous players and then add one more. While games like this were played in many cultures, The Twelve Days of Christmas is probably of Gallic origin.
Some other interesting items about the song are noted in The New Oxford Book of Carols. The cally- or colly-birds in the song are blackbirds. The gold rings, which seem out of place in the list, are most likely a corruption of goldspinks, which is the Scottish-dialect term for goldfinches. Originally, then, the gifts for the first seven days were all birds.
In this activity, students are asked to do two things. First, they must find the total number of gifts. To do this, they need to assume that for each day, the gifts given on the previous day are given again. For example, the gifts for the third day include not only the three French hens, but also two more turtle doves, and another partridge in a pear tree. Students will need to decide whether to count the partridge in a pear tree as one gift or two.
The second thing that students are asked to do is to find the total cost of the gifts. This part of the activity is very open-ended. You may want to assign an arbitrary cost to each gift. For example, you might decide that a partridge in a pear tree costs $1, a turtle dove costs $2, a French hen $3, and so on. A more challenging approach would be to have students come up with their own prices. These prices can be arbitrary or realistic (reflecting the actual cost of such items today). This latter approach would involve some interesting research.
According to an article in Fortune magazine (January 12,1992), the 1991 value of the gifts given on just the twelfth day was $35,949.77. According to the San Francisco investment firm of Hugh Gee and Company, which has been keeping yearly tabs on this information since 1981, this was up 22% from the year before. It is interesting to note that much of the cost increase between 1990 and 1991 was for seven swans, which went up 186% to $7000! Evidently, it had been a bad breeding year for swans.
We hope that you and your students have fun with this activity and that you all will have very happy Holiday Season!