Last March, on Pi Day (March 14, 2015), I put together a mathematical magic show for the Pi Day festivities at our local library, compiling various tricks that I teach to our future secondary teachers. I was expecting an audience of junior-high and high school students but ended up with an audience of elementary school students (and their parents). Still, I thought that this might be of general interest, and so I’ll present these tricks as well as the explanations for these tricks in this series. From start to finish, this mathematical magic show took me about 50-55 minutes to complete. None of the tricks in this routine are original to me; I learned each of these tricks from somebody else.
For my first trick, I chose the most boring of the routine. Everyone in the audience had a piece of paper and many had calculators. I also had a small white board to write on at the front of the room. I began,
To begin this trick, write down any three-digit number on your piece of paper. Just make sure that the first digit and the last digit are different.
After waiting 10 seconds, I then said,
Now, reverse the digits and write down a new number. For example, if your number was 321, the new number will be 123.
And, to be sure my instructions are clear, I’ll write these numbers on my white board:
Next, I’ll say:
Now, subtract the small number from the big number. If your second number is larger, then put that number on top so that you can subtract the two numbers.
After waiting a minute or so, I’ll say,
Your difference is probably a three-digit number. However, if you ended up with a two-digit number, you can make it a three-digit number by putting a 0 in the hundreds place.
Next, I want you to reverse the digits of the difference to make a new three-digit number. Write this new number under the difference.
After everyone’s done, I’ll give my final instruction:
Finally, add the last two three-digit numbers that you wrote down.
After everyone’s done, I’ll point to someone and say, “Your final number was 1,089.” If he followed my instructions and did the arithmetic correctly, he’ll say, “You’re right.” Then I’ll point to someone else and say, “You also got 1,089.” She’ll also say, :”You’re right.” Then I’ll say, “Everyone got 1,089, right?”
Another (and more dramatic) way to end the routine is to hand a book of mine to someone, with the following instructions:
Your last number should have four digits. Cross out the last digit; you now will have a number with only three digits. Turn to that page number in this book. Then find the word on that page corresponding to the number you crossed out. For example, if you crossed out a one, point to the first word on the page. If you crossed out a two, point to the second word on the page. And so on.
Got it? The word you’re pointing to is XXXXXX.
And of course, I’ll get this right because, before starting the routine, I had already memorized the ninth word on page 108 of my book (the XXXXXX above). This looks really dramatic because it looks essentially random to the audience.
In tomorrow’s post, I’ll explain how the trick works.