Maths Trick - Guess the missing number

1. Ask your friend to think of or write down any number that contains more than 3 digits.

Lets say, s/he has written 18274.

2. Ask him/her to add all the digits.

1 + 8 + 2 + 7 + 4 = 22

3. Ask him/her to subtract this number (from step 2) from the original number (from step1).

18274 - 22 = 18252

4. Ask him/her to select any digit from this new number (step 3) and strike it out.

Lets say, s/he selected digit 5. So, resulted number is 1822

5. Ask him/her to add the digits of the resulted new number (that is resulted by striking out).

1 + 8 + 2 + 2 = 13.

6. Ask him/her to tell you the sum and that you would tell the strike out / selected digit.

With the help of this number, you can guess the digit your friend has strike out / selected. Just subtract the number from the next multiple of 9. Here, next multiple of 9 is 18 and hence the digit that your friend had strike out is 5 (=18 - 13).

Wondering how it works? The trick is very simple and it uses the property of 9 - a number whose digits sums up to 9, is multiple of 9.In the above trick,

• Step 1 - 3: By subtracting the number with sum of its digits, we are making the number a whole multiple of 9. Here, 9 x 2028 = 18252.
  
• Step 4 - 5: We have two cases, resultant number obtained by striking out being multiple of 9 or not multiple of 9 as in the example here.
• Non Multiple of 9: By striking out a digit (5) from the number (18252, we are making the resultant number (1822) to be not divisible 9 and difference of, sum of the digits, of the new number and the old number will be exactly less by the striked out digit. i.e., (1+8+2+2) - (1+8+2+5+2) = 5.
• Multiple of 9: This is possible only when the number striked out is 0 or 9. So, in such cases you can simply tell your friend that s/he has striked out either 9 or 0.

Have fun playing the trick on your friends.