Tag: Andrew Stapleton

Guest Post: The Missing Digit Puzzle

Prof. Andrew Stapleton at U. of Wisconsin-LaCrosse shares this teaching tip to enliven your class

This math puzzle looks a lot more intimidating than it really is. It is called the Missing Digit Puzzle. Pick a student to come to the front and write down a number on the white board or overhead projection. Hide or otherwise cover your eyes in some way so that you can’t see what your student is writing.

Ask your student to secretly write down ANY number (at least four digits long). e.g. 78341
Ask her to add up the digits… e.g. 7+8+3+4+1 = 23 … and then subtract the answer from the first number e.g. 78341 – 23 = 78318
Ask her to then cross out ONE digit from the answer. (It can be any digit except a zero) e.g. 7x318
She then reads out what digits are left e.g. 7-3-1-8. Even though you haven’t seen any numbers, you can say what the missing digit is! EIGHT

THE SECRET:
This great puzzle relies on the power of 9.
After your student has added up the digits and subtracted them, the answer will ALWAYS divide
by 9. If a number divides by 9, then when you add the digits up, they will also divide by 9. If
you check our example 7+8+3+1+8 = 27 which does divide by 9. When she crosses a digit
out, she then reads out the digits that are left. You add them up. In the example we had 7+3+1+8
= 19. All you do now is see what you have to add on to your answer to get the next number that
divides by 9! The next number to divide by 9 after 19 is 27. So, you need to add on EIGHT to
get to 27. This is the number that was crossed out!

Here’s another example:
Say the number written down is 873946284 (yikes!).
Your friend adds the digits 8+7+3+9+4+6+2+8+4 = 51
Your friend does the subtraction: 873946284 – 51 = 873946233
(So far you have NO IDEA what numbers are whizzing around!)
Your friend crosses a digit out 87394x233 and tells you what’s left.
You add 8+7+3+9+4+2+3+3 = 39.
The next number that divides by 9 after 39 is 45. As 45-39=6 this means that SIX is the missing
digit.
You can do this one quickly and even have other students come up and give it a try – and you
will always be able to tell what the missing digit is!

Guest Post: An Impressive Two-Minute Math Challenge to Use in Class

Prof. Andrew Stapleton at U. of Wisconsin-La Crosse shares with us a fun teaching tip.

Kick off your class with this captivating two-minute math trick!
Step 1: Grab a calculator. Ask everyone to take out their calculator or open the calculator app on their phone.

Step 2: Create a six-digit number. Instruct each student to think of any three-digit number and repeat it to form a six-digit number. For example: 729 becomes 729729.

Step 3: The magical prediction.  Invite students to shout out their six-digit numbers all at once. Pretend you’re calculating each one in real-time and confidently declare:
“I am going to calculate quickly and give you three directions and you will never have a remainder. That is, each iteration you will have a whole number. Follow my instructions, and your final result will always be your original three-digit number!”

Step 4: The steps.
Have everyone perform these operations on their six-digit number:
Divide the number by 13 (they’ll get a whole number).
Divide the result by 11 (still a whole number).
Divide that result by 7.
Surprise! Each student ends up with their original three-digit number.

How does it work?
The math is straightforward but seems like magic:

Multiplying a three-digit number by 1001 (i.e., 13×11×7) creates a six-digit number by repeating the original. Dividing in reverse (by 13, then 11, then 7) simply uncovers the original three-digit number.

The real fun? Your dramatic prediction adds flair and mystery, making the trick seem far more complex than it is. Enjoy the “wow” moment as your students are amazed!

Guest Post: The Missing Digit Puzzle!

Prof. Andrew Stapleton at U. of Wisconsin-La Crosse shares with us another fun and motivational teaching tip.

This math puzzle looks a lot more intimidating than it really is. It is called the Missing Digit Puzzle. Pick a student to come to the front and write down a number on the white board or overhead projection. Hide or otherwise cover your eyes in some way so that you can’t see what your student is writing.

Ask your student to secretly write down ANY number (at least four digits long). e.g. 78341 Ask her to add up the digits… e.g. 7+8+3+4+1 = 23 … and then subtract the answer from the first number e.g. 78341 – 23 = 78318. Ask her to then cross out ONE digit from the answer. (It can be any digit except a zero) e.g. 7×318. She then reads out what digits are left e.g. 7-3-1-8

Even though you haven’t seen any numbers, you can say what the missing digit is! EIGHT.

THE SECRET: This great puzzle relies on the power of 9. After your student has added up the digits and subtracted them, the answer will ALWAYS divide by 9. If a number divides by nine, then when you add the digits up, they will also divide by 9. If you check our example 7+8+3+1+8 = 27 which does divide by nine. When she crosses a digit out, she then reads out the digits that are left. You add them up. In the example we had 7+3+1+8= 19. All you do now is see what you have to add on to your answer to get the next number that divides by nine! The next number to divide by 9 after 19 is 27. So, you need to add on EIGHT to get to 27. This is the number that was crossed out!

Here’s another example: Say the number written down is 873946284 (yikes!). Your friend adds the digits 8+7+3+9+4+6+2+8+4 = 51. Your friend does the subtraction: 873946284 – 51 = 873946233 (So far you have NO IDEA what numbers are whizzing around!) Your friend crosses a digit out 87394×233 and tells you what’s left. You add 8+7+3+9+4+2+3+3 = 39. The next number that divides by 9 after 39 is 45. As 45-39=6 this means that SIX is the missing digit.

You can do this one quickly and even have other students come up and give it a try – and you will always be able to tell what the missing digit is!