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Pascal's Chrismas Gift

Use Pascal's Triangle to find the number of items given each day in the song The 12 Days of Christmas.

Day 1: One partridge in a pear tree
Day 2: Two turtle doves
Day 3: Three French hens
Day 4: Four calling birds
Day 5: Five gold rings
Day 6: Six geese a-laying
Day 7: Seven swans a-swimming
Day 8: Eight maids a-milking
Day 9: Nine ladies dancing
Day 10: Ten lords a-leapin'
Day 11: Eleven pipers piping
Day 12: Twelve drummers drumming

Question 1: Use Pascal's Triangle to find the number of combined gifts given on each consecutive day. For example, on day 1, it is 1...on day 2, it is 1+2=3, etc.

Question 2:Use Pascal's Triangle to find the total number of gifts given over all twelve days.


Hint: Using red, color in the cells representing the number of respective gifts for each day. Now, use two others colors to color in cells that represent answers to the remaining two questions. Look for a pattern.


Solution Commentary: Rather than presenting a solution here, you need to consider another web site that includes a lesson plan for this problem activity. The lesson, part of the DIMACS site, was created by Judy Ann Brown in 1992.