Missing Digit Math Trick

The Missing Digit Trick!

Ask a friend to secretly write down ANY number (at least four digits long). e.g. 78341.

Ask the friend 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

Your friend then crosses out ONE digit from the answer. (It can be any digit except a zero) e.g. 7x318

Your friend 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 trick relies on the power of 9. How?

After your friend 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 your friend crosses a digit out, he 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. This is the number that was crossed out!

Here's another example: 

• Say the number written down is 873946284.
• 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 x 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 6 is the missing digit!