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!