Chapter 5--Calendar Magic
Chapter 5--Calendar Magic

© 2017 by Jerry L. Croasmun

Herr Specht had a way of turning ordinary objects into math lessons. On one of our very many adventures, he pulled out several calendars from his bag and began talking.

"A lot of life-changing events happened on November 29, 1944. I was born in Potsdam, Germany while the world was at odds with one another in World War II. Nazi forces, under the control of Adolf Hitler, still reigned terror. However, a breath of fresh air and much celebration took place as the country of Albania was liberated from Nazi control on that Wednesday in November of 1944. U.S. Navy Captain Joseph Enright and his crew of the USS submarine Archerfish also sunk the Japanese aircraft carrier Shinano on my birthday."

"Calendars are tools which help us keep track and memorialize important dates in history, but calendars can also teach us a lot about math, patterns, and life." Handing each of us a page from a calendar he asked, "How many days are in a week and how many months are in a year?"

Ben excitedly replied, "Seven. There are seven days in a week. Everyone knows that and there are twelve months in a year."

"Very good, Benjamin," Herr Specht admonished. "Now tell me what 16 + 7 is? You can use your calendar page if you need a hint."

I think the mention of calendar threw Ben and me off a little. After a few moments, Ben said, "Twenty-three. 16 + 7 = 23."

"You certainly know your math, but did you use your calendar?" asked our self-appointed professor. "I noticed you hesitated in giving a response, but a mere glance at the calendar would have provided an instant answer. Let's try another one, but this time look at the calendar and do not try to do the math in your head. What is 21 + 7? Point to your answer on the calendar."

"Math is all about relationships and patterns. Math is magic and today, I am going to show you how calendars are magical too. If you want to know what 8 + 7 is, place your finger on the 8 and move down to the next row or week and you have 15. Likewise, to find the answer to 20 minus 7, move back or up one row or week. I see you both have your finger on the number 28. Very good. Yes, 21 + 7 or 7 + 21 is equal to 28. I think you understand elementary addition and subtraction so let's move on to some real magic. Pick four boxes which form a square and add the four numbers together. Do not tell me your numbers, but rather share your sum and I will magically guess your numbers. For example, the numbers 1 + 2 + 8 + 9 equal 20 when added together. Now you try it."

-- November 1944 --
S M T W Th F S
1 2 3 4
5 6 7 8 9 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28 29 30

Ben was very secretive and did not tell his choice of numbers with anyone until he finally said, "My total is 28."

Herr Specht without hesitating said, "Ben, your numbers are 3, 4, 10, and 11."

My brother and I both were in shock and Ben yelled out, "How did you do that?"

"It is math and it's magic," was the only explanation the little old man provided.

Attempting to stump our math magician, I chose the numbers 22, 23, 29, and 30. After carefully adding the numbers and checking my answer twice, I said, "The sum of my numbers is equal to 104."

"Let's see. 104 divided by 4 is 26. Young lady, your numbers are 22, 23, 29, and 30," Herr Specht said as he winked his left eye.

I heard the number 26 and was beginning to think I had tricked Herr Specht, but once again he proved his intelligence was something to behold. "You are correct. But, how did you do that?" I asked.

"Calendars are magical and contain both math and magic. Magicians rarely reveal their secrets; however, I promise you I will share the hidden magic behind this calendar trick all in due time. First, you two must do some detective work involving inspection and discovery on your own. I will provide guidance, of course, but real learning takes place when one discovers the magic for themselves."

"You both have a 1990 calendar, I want you to separate and arrange the pages so you can see all twelve months at once. Next, organize your calendar pages into stacks according to the number of days in each month. Afterwards sort them in chronological order according to the months of the year. For example: January would be on top and December on the bottom." Herr Specht gave us a few minutes to do as he had instructed and then asked, "How many stacks do you have?"

I answered, "I have three stacks. Those months having 30 days, those with 31, and February is by itself. January, March, May, July, August, October, and December all have 31 days. April, June, September, and November all have 30 days each and February is the exception having either 28 or 29 days. We call that leap year when February has 29 days. Most years there are 365 days and 366 on leap year."

Ben added, "I think I remember a little jingle from elementary school. It went something like, 'Thirty days has September, April, June, and November. All the rest have thirty-one except February.'"

Herr Specht acknowledged our responses and then instructed us to, "Sort the months into stacks which start on the same day of the week. For example, if April 1st and May 1st are both on a Monday, place them in the same pile."

I began to look through the pages and realized our German friend had given us a beautiful calendar with photographs from his native country. I also noticed many of the German months looked similar to their English counterparts. I began to read or sound out, "Januar, Februar, März, April, Mai, Juni, Juli, August, September, Oktober, November, Dezember." Herr Specht graciously interjected and helped with my pronunciation.

Ben then added, "I have discovered with this 1990 calendar the months of May, June, and August do not have anything in common. Whereas, January and October; February, March, and November; April and July; and September and December all begin on the same day."

"Ben, you have clearly unraveled one of the mysteries to the calendar magic. First, you need to know how many days are in each month and then you will be able to begin recognizing the patterns. This year's calendar does not contain February 29th so you are correct. However, when I was born in 1944 it was a leap year so the patterns are different. The last leap year was in 1988 and the next one will be in 1992, 1996, 2000, 2004, etc. January, April, and July all follow the same pattern on leap years in addition to February and August; September and December; March and November. During a leap year May, June, and October do not share anything in common with any of the other months. Knowing the patterns is fun and informative since we know April and July always share the same days we know there will be another Friday the 13th this July."

"Another way to remember how many days each month has is to make a fist and to count your knuckles. In Germany we use one hand and begin counting with the knuckle on the left as January, the valley or crevice would be February, and the next knuckle as March, etc. Knuckles or bumps have 31 days and valleys or crevices have 30 with February being the exception. Some countries also use two hands to teach kids the knuckles mnemonic."

"Now for some more calendar magic," said Mr. Woody. "Take a calendar and choose any 9 days that form a 3 by 3 square like this one," he said while drawing a square around the numbers 7, 8, 9, 14, 15, 16, 21, 22, and 23.

7 8 9
14 15 16
21 22 23

"Now add all nine numbers together and divide the sum by nine. You will get the number in the middle, which in our case is 15. When we add 7 + 8 + 9 + 14 + 15 + 16 + 21 + 22 + 23 we get 135. The sum of 135 divided by 9 is equal to 15. Once you know the number in the middle you can fill in the rest of the calendar. It is magic and it is all about relationships. For example: The day before the 15th is the 14th and the day after the 15th is the 16th."

"You could also have the person divide their total by the middle number and they will always get nine as an answer. You could call it the magic 9 squares or something clever like that. The magic will only work if the person you are sharing your magic with is able to add and divide their numbers accurately."

"I find it fascinating that you can add the three numbers in the center row, the three numbers in the center column, and add the three numbers diagonally in both directions and you will come up with the same answer. In our example: 14 + 15 + 16 is equal to 45, 8 + 15 + 22 also equals 45 and adding the three numbers diagonally left-to-right; 7 + 15 + 23 = 45 and diagonally from right-to-left; 9 + 15 + 21 equals 45. It is magic and it will work for any three-by-three square of nine calendar dates."

"Wow, Herr Specht, that is magical," I said. "I also noticed that the middle number in our case is 15 and when we divide the sum of 45 by 3 we get 15. Does that always happen?"

"Yes, when you add the three numbers and divide by three you will always get the middle number," answered Herr Specht. He then asked, "Do you kids know what kind of calendars we are using?"

Ben excitedly said, "They are German calendars and start with Monday instead of Sunday."

I added, "They are beautiful and make me want to visit your Germany." I then began trying to say the days of the week in German, "Montag, Dienstag, Mittwoch, Donnerstag, Freitag, Samstag, Sonntag."

       -- Mai 1990 --       
Mo Di Mi Do Fr Sa So
1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30 31

The little man chuckled at our responses and said, "I am glad you like the calendars and hopefully you both will one day be able to see those spectacular places for yourselves. Most of the modern world now use the Gregorian Calendar. Prior to the Gregorian Calendar the Julian Calendar, named after Julius Caesar, was used. A year is roughly the amount of time it takes the Earth to orbit the Sun and a month is how long it takes for the moon to orbit around the Earth. The German word for month is monat."

"The Gregorian Calendar is named after the Catholic Pope Gregory XIII. In October of 1582, he introduced the calendar as a way of aligning Easter with the spring equinox. Many protestants were suspicious of the Pope and it wasn't until 1700 that Germany adopted the calendar. Great Britain and the American Colonies followed suit by an act of Parliament as signed and approved by King George II that declared Wednesday, September 2, 1752, was to be followed by Thursday, September 14, 1752. Calendars are fun and magical with eleven days in 1752, having vanished or disappeared as if they never existed. Greece was the last country to adopt the Gregorian Calendar in 1923."

"I never realized there was so much history with calendars. The one we use now is the only one I knew existed. After all it has been the only one for my entire life," I said.

"Mine too," said Mr. Woody. "Many of the months are named after Roman Gods, deity, or festivals with July being named for Julius Caesar himself. Juno is the queen of gods and patroness of marriage and weddings and to this day many still tie-the-knot during the month of June. March is named for Mars the Roman god of war and May is named after Maia an earth goddess of growing plants. The months of September, October, November, and December all are named after when they originally occurred in the ancient Roman calendar. Check it out sometime."

"My favorite month is October," Ben said. "It has Halloween and my birthday is on October 5th. I can hardly wait until my birthday this year I am going to be fourteen and America is going to be 214 years old. I remember because I was born in 1976 on America's Bi-centennial. I still have some Bi-centennial quarters. "

"How many sides are on an octagon, how many tentacles does an octopus have, and how many sides are on a stop sign?" asked the old man.

"I remember learning this in school," I said. I believe, the answer to all of your questions is eight because the latin word octo means eight."

"You are correct, but why is Oktober the tenth month instead of the eighth? And why is Dezember the twelfth month if decem is latin for ten?" asked Herr Specht.

"I don't know. So tell us why, Herr Specht," Ben said.

The little man obliged by saying, "Under the Julian Calendar, Oktober was the eighth month and Dezember was the tenth month. The names are hold overs, but they were moved down in the order. I think it is time to reveal the magic to the four-by-four square. Remember earlier when I had you pick four numbers and add the numbers together? Well, the trick or magic is all in the number four. If you have four squares, you can divide the sum by four and then subtract four to get the answer for your first square. The rest is merely Algebra or adding and combining like terms to find the number. I think I will save 28 = n + n + 1 + n + 7 + n + 8 or 28 = 4n + 16 for another day."

Ben and I both said, "Thank you," in unison.

"Remember kids, calendars are magical and if we keep our 1990 calendars we can reuse them again in 2001, 2007, and 2018," said Herr Specht.

3 4
10 11

28 = n + n + 1 + n + 7 + n + 8

28 = 4n + 16

28-16 = 4n + 16 -16

12 = 4n

12/4 = 4/4n

3 = n

n = 3; n + 1 = 4; n + 7 = 10; n + 8 = 11

Read Chapter 1--Fraction Bar
Read Chapter 2--Pizza Pi
Read Chapter 3--Helen Marie
Read Chapter 4--The Wall Of Division
Read Chapter 5--Calendar Magic

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(NIV) Scripture taken from the HOLY BIBLE, NEW INTERNATIONAL VERSION.
Copyright (C) 1973, 1978, 1984 International Bible Society.
Used by permission of Zondervan Bible Publishers.