Here’s a neat little trick I came up with.

Effect: You write down a fairly long (i.e. six-digit) number on a scrap of paper and put it face down on the table. Then you have your friend write down a single digit (1-9) on a piece of paper. Beneath it, you write down a two-digit number. Your friend then writes a three-digit number (anything between 100 and 999 will work nicely). Then you write a four-digit number. Then your friend writes a five-digit number. Then you write a six-digit number, and you have your friend add up all six numbers. Then you flip the first paper face up to reveal the number you had written at the very beginning, which (if nobody messed anything up) should match your friend’s sum. (Unfortunately, it is very easy for something to go wrong. If the numbers don’t match, check the sum with a calculator because it might just be a simple computational error.)

How to do the trick: (Hopefully this explanation is clear enough.) Before performing the trick, you need to choose a three-digit number and make sure you remember it throughout the trick! To keep things easy, do not choose a number which has any 9’s in it. It is also best not to include any 0’s either. For this example, we will use 123. When you begin the trick, you need to do the following mental calculations to convert this number into your initial six-digit number: first reverse the digits (to get 321); and then add 1 to each digit (such that 321 becomes 432); then stick a zero after each digit (to get 403020), and then subtract 3 (to arrive at 403017, which is the number that you need to write down on the first scrap of paper, which should be kept face-down for dramatic effect). Then during the trick, the numbers that your friend writes can be whatever he wants so long as they have the correct amount of digits (ideally your friend will not choose numbers with repeating digits such as 99999, but it’s ok if he does). However, the numbers that you write down need to be carefully constructed according to the following rules: The first number that you write down is going to be two digits: the first digit needs to match the first digit of your original three-digit number (in this case you’d use 1, because 1 is the first digit of 123) and the second digit needs to be the 9’s complement of whatever number your friend wrote down (i.e. if your friend wrote 1 then you’d write an 8; if your friend wrote 2 then you’d write 7, and so on; basically your friend’s number plus your number need to add up to 9: see this table; so if he writes a 5 then you write 4). And then do the same for the other numbers: Your second number is going to be four digits, which will be the second digit of your original three-digit number (in this case the 2 from 123) followed by a three digit number constructed from the 9’s complement of each of the digits in your friend’s three-digit number. And your final number is going to be the third digit of your original number (i.e. the 3 from 123) followed by a five-digit number corresponding to the 9’s complements of your friend’s five-digit number.

Example playthrough:

         5    <-- friend
        14    <-- you
       836    <-- friend
      2163    <-- you
     14804    <-- friend
    385195    <-- you

(You need to practice this trick a lot and get comfortable with the 9’s complements, because it’s not supposed to look like you are doing any mental calculations during the trick but it’s supposed to look like you’re just pulling numbers out of thin air. The good thing about this trick is that it can be repeated using a different three-digit starting number each time such that the sum comes out to something else, but you probably shouldn’t repeat the trick more than twice in one sitting or somebody might be able to figure out what’s going on.)

Why does the trick work? How about you try and figure it out for yourself 😉