Happy Pi Day, folks! I’m departing from the usual pi day talk of circles and desserts to discuss fun with algebra, just like I promised in yesterday’s blogiversary post.
You’ve probably seen this kind of “jedi mind trick” in a forwarded e-mail or a shared Facebook post:
Think of a number. Add 3. Multiply by 2. Square it. Subtract 36. Divide by 4. Divide by your original number. Subtract your original number.
Your answer is 6.
It’s nifty, but it’s more of a jedi math trick than a jedi mind trick.
Specifically, it’s a jedi algebra trick. Let’s use x instead of a specific number.
Think of a number.
x + 3
Multiply by 2.
2*(x + 3) = 2x + 6
(2x + 6)^2 = (2x + 6)*(2x + 6) = 4x^2 + 24x + 36 (Remember the acronym FOIL? We’ll definitely discuss it at greater length another day, but the quick version is this: (a + b)*(c + d) = ac + ad + bc + bd. It works with integers as well as variables. What’s six times eight? Now let’s use what we just said about FOIL to calculate (2 + 4)*(3 + 5): (2*3) + (2*5) + (4*3) + (4*5) = 6 + 10 + 12+ 20 = 48)
4x^2 + 24x
Divide by 4.
x^2 + 6x = x*(x + 6) (Notice that when we multiply everything inside the parentheses by the x outside the parentheses, we get the expression we started with.)
Divide by your original number.
x + 6
Subtract your original number.
Algebra is awesome.
Now that we’ve finished the algebraic proof for that trick, I’m issuing you all a challenge:
Take any two-digit number. Reverse the digits. Add these numbers together. Divide by the sum of the digits of your original number. You’ll always get 11. Your challenge: use algebra to show why this is true.
Nifty math tricks like this always remind me of this book, which my fourth grade teacher/elementary school math club advisor lent me. (Incidentally, this was the same teacher who, through the use of puns, first taught me about pi.) Even as a child, I think I hated the subtitle of the book, but I did love the quirky calculations I learned. I think I went around for weeks figuring out what day of the week everyone was born on.