Wednesday, December 18, 2013

And the winner is ...

On Monday we posed a riddle to you, regarding the total, cumulative number of gifts in the well known song The Twelve Days of Christmas. 

Here's the song:

For this puzzle, you were asked to come up with the total cumulative number gifts received by the giftee on the third, seventh, and twelfth days. 

The library received an avalanche of emails, but only 7 of the emails received had the correct answer. 

On the 3rd day, the giftee had received 10 gifts.
On the 7th day, the giftee had received 84 gifts.
On the 12th day, the giftee had received 364 gifts.

Many of you got the correct numbers for each day (6 gifts on the 3rd day, 28 gifts on the 7th day, and 78 gifts on the 12th day), but you forgot to add those gifts to the ones the giftee already had. 

On the first day of Christmas, the giftee got 1 gift.
On the second day, the giftee got 3 gifts -- but s/he already had 1, so the total for that day is 4. 
On the 3rd day, the giftee got 6 gifts. Added to the 4 s/he already had, that brings the cumulative total for the 3rd day to 10 gifts.  By adding the gifts received on a specific days to the gifts already in the giftee's possession, we arrive at the correct answers. 

The numbers in this song (1,3,6,10, etc.) are called triangular numbers. Click here to see an explanation of triangular numbers and to see the sequence of the first hundred. You will recognize the first 12 as the gifts received each day in the song.  

And now for the winner of this contest!

The winner of the Hershey's large chocolate bar is..... Dawn Niles! Congratulations, Dawn! Please come to the library to get your prize. 

But wait, there's more! 

The entries below were all correct, and although they came in after the winning entry, they have all received honorable mentions, and the senders have each won a candy bar. Please come to the library to collect your prize!

Jennifer Beiner
Dolan Harrington
Lee Bobbio
Mary Hedges
Danielle Taylor
Chiron Anderson

Prizes must be collected by 4:30 p.m. on Friday, December 20th.