Maths Trick - Guess the result - 1089.

1. Ask your friend to think of or write down any 3 digit number such that the digits are in ascending order (highest to lowest) and that they are not repetitive. 

    Lets say, s/he has written 765. While your friend is writing down the number, you write down 1089 and don't show it to your friend.

2. Ask him/her to reverse the number and subtract it from the original number (step1).

    765 - 567 = 198

3. Ask him/her how many digits the result has. If it has 3 digits, ask him to reverse the result and if it has only 2 digits, then ask him to add a zero in front of it and then reverse the digit. Ex Number - 099  reverse number - 990

    Here it is 3 digits, and hence reverse number is 891

4. Ask him/her to add this number (from step 3) to its previous number (from step 2 - obtained by doing subtraction) and ask him/her not to tell you the result.

    891 + 198 = 1089

5. Now you can reveal the number (written by you in step 1) which is an exact match of their result (step 4)

Curious to know how it works? It is simple, just read the below explanation.

By asking your friend to subtract the original number from the reversed number, you are making the number indirectly multiple of 99. 

Say the Original number is xyz = 100x + 10y + z

Therefore, Reversed number is zyx = 100z + 10y +x

Subtracting these both, xyz - zyx = (100x + 10y + z) - (100z + 10y +x) = 99x -99y = 99 (x-y)

Now, if you see the below 99 table you can see that (A.) Products are digit reversals of each other, that is 99 x 6 = 594 which is reverse of 495 = 99 x5. Such is the case with others. Therefore (B.) the result of adding the number with its reversed number is always 1089.

99 x 2 = 198 + 891 = 1089

99 x 3 = 297 + 792 = 1089

99 x 4 = 396 + 693 = 1089

99 x 5 = 495 + 594 = 1089

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99 x 6 = 594 + 495 = 1089

99 x 7 = 693 + 396 = 1089

99 x 8 = 792 + 297 = 1089

99 x 9 = 891 + 198 = 1089

99 x 10 = 990 + 099 = 1089

Have fun playing the trick on your friends.