How Many Handshakes?

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

As long as they don't share milkshakes.

If you draw the diagonals of an octagon then each point will touch each of the other 7 points. If you counted all the lines (which Mike hasn't drawn yet), you would get 28 of them. A touches 7, B touches A, which we already counted, and 6 more, C touches 5 more, D touches 4 more, E touches 3 more, F 2 more, and G 1 more. So 7 + 6 + 5 + 4 + 3 + 2 + 1 = 28.

Or through the Counting Principle, 8 * 7 is 56 handshakes, but since it takes two to shake and we don't care who shook whose hands first, we divide that number by 2 and get 28 again.

How much sanitizer do they need? That's up to each individual, but it probably isn't enough. Until it's too much.

I also write Fiction! You can now preorder Devilish And Divine, edited by John L. French and Danielle Ackley-McPhail, which contains (among many, many others) three stories by me, Christopher J. Burke about those above us and from down below. Preorder the softcover or ebook at Amazon. Also, check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides. Available in softcover or ebook at Amazon. If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads.

Come back often for more funny math and geeky comics.

How Many Launches?

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

Assume a giant space amoeba doesn't swallow up the entire system first.

Solutions are left as an exercise for the reader.

Nah, that's not a copout. I'm just trying to get more comments.

I also write Fiction! Check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides. Available in softcover or ebook at Amazon. If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads. Thank you.

Come back often for more funny math and geeky comics.

How Many Lunches?

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

What? No appetizers or antipasto?

For those unable to read the fine print on the menu (sorry, but it had to shrink to fit), the questions asks, "How many combinations of a main course, a vegetable, a side and a dessert can be made from this menu?"

The Counting Principle tells us that the number of possible combinations of one item from each list is equal to the product of the number of items in each list. I did a video on this for a grad school class. When I showed it a several years later, my AP remarked that I looked the same. When I showed it in a different school three years later, my coteacher said, "Mr. Burke, you look so young!" I thnk that was meant as a compliment.

In this particular instance, however, there are 3 choices for a main course, despite what you think of the pizza or the tuna, 2 choices for a vegetable, which no one said had to taste good to be good for you, 4 desserts, and 3 beverages. According to the Counting Principle, that means that there are 3 * 2 * 4 * 3 = 72 choices.

If you found this page by googling a question on your state exam, please not that I altered the question to suit this comic. Your teacher may be expected a different answer than I have provided.

I also write Fiction! Check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides. Available in softcover or ebook at Amazon. If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads. Thank you.

Come back often for more funny math and geeky comics.

Pascals Triangle

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(C)Copyright 2015, C. Burke.

The ₁₄C₃ gifts of Christmas?

This occurred to me a while ago, but after Christmas, and I decided that it couldn't wait until December. (And I'd likely forget about it.)

While coming up with mathematical formulas and computer code for calculating this number, I overlooked a a very reliable reference tool: Pascal's Triangle.

It has more uses than simply expanding polynomials because of its many properties.

Some of these properties are as follows:

The "zeroth" element of each row is the number 1.

The first element of each row is the number of the row (keeping in mind that the top row is Row 0).

The second element of each row is are the consecutive triangle numbers, the sum of the consecutive numbers before it.

Which makes the third element of each row the sum of the consecutive triangle numbers.

And, finally, the position of each element in Pascal's Triangle corresponds to the number of Combinations designated by the notation _nC_r where n is the row and r is the element of that row.

What this means is that for any given day in that song (The Twelve Days of Christmas):

_nC₁ refers to the day we're up to. On Day 7, ₇C₁ is 7.

_n+1C₂ refers to the total number of gifts given on the nth day. On Day 7, ₈C₂ is 28.

_n+2C₃ refers to the total number of gifts given altogether up to the nth day. On Day 7, ₉C₃ is 84.

Applying this to the 12th day of the song:

₁₂C₁ is 12.

₁₃C₂ is 78.

₁₄C₃ is 364.

And I could've been finished a whole lot sooner. But I wouldn't have gotten a recursive comic out of that.

One last thing: Did you ever try to make a poster of Pascal's Triangle? Have your students tried to do it for a math fair? The numbers start to get really big in the middle, really fast. (That's a post for another day.) But that's also why the poster in this comic is so large! Otherwise, it wouldn't be readable (and I had to modify the "364" so you could find it easily!).