30 May 2018

Lightning addition (version 2)

Ask the person to which you will perform the trick to choose two different digits. Tell him to add them. Then tell him to add the last digit (of the first two digits) to the result obtained. The person should perform the same sequence of addition until he/she gets \(10\) numbers.

Example:

\(3+7=10\;,7+10=17\;,10+17=27\;,17+27=44 \ldots\)

Ask for the person to show the list of \(10\) numbers obtained. Now ask him/her to calculate the sum. After \(5\) seconds you should say the result, which for our example is \(2,046\).

How can we know the result so fast? The trick is that the sequence of numbers obtained follows a Fibonacci Sequence. To achieve the desired sum, we need only to multiply the seventh number of the sequence by \(11\). Thus, \(186 \cdot 11 = 2,046\).

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