I love Numberphile!
A great thing with this trick is that it scales up very easily. If you want to sum a total of seven numbers, (your starter, plus three from your friend and three from you) just add 30,000 to your starter and then subtract three. For nine numbers, add 40,000 and subtract four.
You can also scale up the length of the numbers. For a total of five five-digit numbers, add 200,000 and subtract two. For five six-digit numbers, add 2,000,000 and subtract two.
Then, of course, you could combine the scaling mechanisms. So, to sum a total of eleven seven-digit numbers you would add 50,000,000 and subtract five.
To add another spin to it, you can mix up the order in a few ways. For a five-number sequence, any of the following orders could be used, where Y is You and F is your Friend:
- YFYFY (as seen in the video)
You just need to make sure that your complementary numbers (in this case, I use the term to mean a number that adds with your friend's number to make 9,999) are always somewhere after the number it needs to complement in the sequence, and that you have one more input number than your friend.
So, a seven-number sequence could go:
- YFYFYFY (similar to the video)
...And probably a few other ways I just can't think of right now. What you definitely don't want to happen is something like:
...etc. In each of these cases, your friend will have some inputs where you will not have an opportunity to follow-up with a complement.
Mixing things up like this, and running the trick several times in several different ways, will help to keep your friends scratching their heads and thinking you really are a genius!