Christmas is a golden and joyful opportunity for number enthusiasts and math geeks to sharpen their creative mathematical problem-solving skills.
Here are 12 CHRISTmaths cookies that may help you shake your brain a little bit in the midst of Christmas festivities.
Warning: Refrain from forwarding this post to relatives or friends living in countries, which are intolerant of Christmas and Christianity, such as Brunei, Saudi Arabia, and Somalia, as it’s haram for “infidels” to take part in any kind of Christmas celebrations. And I assume that includes reading any on-line materials deemed un-Islamic or un-Mohammedan, which might lead believers astray from the faith.
1. Unlucky Turkeys
Estimate the number of turkeys that make their way to the supermarkets every year.
2. A Xmas Candy
Mary wanted to buy a candy that costs 25 cents. A dated vending machine would take one-cent, five-cent, and ten-cent coins in any combination. How many different ways can she use the coins to pay for the candy?
3. The Dimensions of a Cross
A square of side 25 cm has four of its corners cut off to form a cross. What is the perimeter of the cross?
4. The Number of Crossings
Two lines can cross one time, three lines three times, four lines six times, and five lines ten times. If there are 25 lines, what would be the maximum number of crossings be?
5. An Eco-Xmas
If all instances of the word “CHRISTMAS” were replaced with “XMAS,” how much ink and paper (or Xmas trees) could you save every year? How much money could be channelled back to feeding the poor and the hungry during the festive season?
6. Number of Xmas Cards
In an age of Xmas e-cards and video cards, how many Christmas greetings cards are still being sent worldwide? How many trees are being saved every festive season?
7. Does Xmas! have 25 digits?
1! = 1, 2! = 1 × 2 = 2, 5! = 1 × 2 × 3 × 4 × 5 = 120—a 3-digit number, and 10! = 1 × 2 ×⋯× 10 = 3,628,800—a 7-digit number.
(a) Without a calculator, how would you verify whether the number 25! has precisely 25 digits or not.
(b) Which positive integers n (other than the trivial case n = 1) for which n! has exactly n digits?
8. Xmas Trees
Guesstimate how big a forest would 25 million Christmas trees occupy.
9. Folding papers
Fold a single piece of paper perfectly in half, from left to right. How many creases will there be after the 25th fold, when you continue folding so that all the rectangles are folded into two halves each time?
10. Pre-Xmas Tax
Imagine Singapore were to implement a pre-Christmas tax on all kinds of Christmas marketing before the first week of December. Estimate how many extra million dollars would the Income Tax department collect every festive season.
11. A Xmas Quickie or Toughie
What is the sum of the last two digits of 1! + 2! + 3! +⋯+ 24! + 25!?
12. An Ever-Early Xmas
Show that as one celebrates more and more Christmases (or, as one gets older and wiser), Christmas seems to come earlier every year.
Gould T. (2013). You’re all just jealous of my jetpack. New York: Drawn & Quarterly.
Yan, K.C. (2011). Christmaths: A creative problem solving math book. Singapore: MathPlus Publishing.
Zettwoch, D., Huizenga, J., May, T. & Weaver, R. (2013). Amazing facts… & beyond! with Leon Beyond. Minneapolis: Uncivilized Books.
A Xmas Bonus: 25 CHRISTmaths Toughies from Singapore ?? http://tinyurl.com/q9w3ne9
Selected Hints & Answers
2. 12 ways. Hint: Make an organized list.
3. 100 cm.
4. 300 crossings.
5. About 30 million gallons of ink, 500 square miles of paper, and $15 trillion could be saved.
7. (b) n = 22, 23, 24.
9. 225 – 1.
12. Hint: Why as one gets older, time appears to fly faster.
© Yan Kow Cheong, December 25, 2015.