Give a volunteer from the audience an envelope with a prediction.
Show 9 cards numbered from 1 to 9. Ask a member of the public to choose 3 cards.
Write the chosen numbers on a board or sheet of paper. For example, if the numbers 2, 5 and 8 have been chosen, the rule is to put the largest number on the left (but this instruction should not be communicated).
Write down the number 852.
Now ask them to subtract the inverse, i.e. 852 - 258. Write the result 594 and add the symmetric.
Write down the result 1089.
Now ask the person you gave the envelope to open it and ask them to read the number written on it: it's 1089.
Let us assume that the initial number is the larger and has digits a, b and c. So, when we reverse and subtract we will have (100a + 10b + c) – (100c + 10b + a)
This is the same as 100a + 10b + c – 100c – 10b – a = 99a – 99c = 99(a – c)
Because a and c are integer numbers, at the end of the first part of the process we will always end up with a multiple of 99.
The three digit multiples of 99 are: 198, 297, 396, 495, 594, 693, 792 and 891.
Now, note that the first and last digits of each number add up to 9.
So, when we reverse any of these numbers and add them together we get 9 hundreds from the first digit, 18 dozens from the second digits and 9 units from the third digit.
So we get 900 + 180 + 9 = 1089.