How to fake a super brain

Fun with Fibonacci sequences

Would you like to be able to impress your friends and family with your amazing mathematical skills? Now is your chance. Here is a rather cunning maths magic trick that uses the power of something called a Fibonacci sequence to do all the hard work for you.

Performing the amazing mathematical brain trick

First select a person to impress. Ask them to write down any two numbers (say both less than 30) one under the other. Suppose they chose the numbers 16 and 21. They write these two numbers under each other

16
21

Now ask them to add these two numbers together and write the total under the first two numbers. After a bit of mental arithmetic they write

16
21
37

Now you ask them, having just added the first and second, to add the second number to the third number in the list: that is 21 + 37 for our example. They must write that new total under the numbers in the list. So they now have

16
21
37
58

Now we step up a gear. Have them do this same thing again and again, adding the last two numbers each time until there are 10 numbers in the list. They may need to resort to button pressing on a calculator. That's fine, and all the better to show your maths super powers if they are finding it hard. Look away while they are doing the later numbers, so they don't think you are up to anything. When they have 10 numbers in the list you turn back and prepare to impress.

The final list of 10 for our example looks like this

16
21 
37 
58 
95 
153 
248 
401 
649 
1050

You are going to instantly find the sum of these 10 numbers. They can start to add them on their calculator, but you will beat them to the answer, 'It's 2728' you say, and what's more after the buttons are pressed and the additions done on their machine they see you are right!

But how has this illusion of super maths power been possible?