. . . . . Lightning Addition
Give your volunteer a sheet of paper, a pencil and a calculator.
Then give him these instructions.
Number the lines from 1 to 10.
On the first line, write any one-digit number.
On the second line, write any two-digit number.
On the third line, write the sum of the 1st and 2nd numbers.
On the next line, write the sum of the 2nd and 3rd numbers.
On the next line, write the sum of the 3rd and 4th numbers.
And so on until he has filled the 10 lines.
Have him add the ten numbers.
After a glance a his list, you can predict the total.
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Secret: Multiply the 7th number by 11.
The reasoning is obvious in the listing.
Let \(\displaystyle a\) and \(\displaystyle b\) be the first two numbers.
. . \(\displaystyle \begin{array}{ccc} 1 & a\\ 2 &b\\ 3& a+b \\ 4 & a+2b \\ 5 & 2a+3b \\ 6 & 3a+5b \\ 7 & 5a +8b & \Leftarrow \\ 8 & 8a+13b \\ 9 & 13a + 21b \\ 10 & 21a+ 34b \\ \hline \text{Total}& 55a+88b &\Leftarrow \end{array}\)
I bet you didn't know that the Fibonacci series
. . could be used for a show-off stunt.
*
Give your volunteer a sheet of paper, a pencil and a calculator.
Then give him these instructions.
Number the lines from 1 to 10.
On the first line, write any one-digit number.
On the second line, write any two-digit number.
On the third line, write the sum of the 1st and 2nd numbers.
On the next line, write the sum of the 2nd and 3rd numbers.
On the next line, write the sum of the 3rd and 4th numbers.
And so on until he has filled the 10 lines.
Have him add the ten numbers.
After a glance a his list, you can predict the total.
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Secret: Multiply the 7th number by 11.
The reasoning is obvious in the listing.
Let \(\displaystyle a\) and \(\displaystyle b\) be the first two numbers.
. . \(\displaystyle \begin{array}{ccc} 1 & a\\ 2 &b\\ 3& a+b \\ 4 & a+2b \\ 5 & 2a+3b \\ 6 & 3a+5b \\ 7 & 5a +8b & \Leftarrow \\ 8 & 8a+13b \\ 9 & 13a + 21b \\ 10 & 21a+ 34b \\ \hline \text{Total}& 55a+88b &\Leftarrow \end{array}\)
I bet you didn't know that the Fibonacci series
. . could be used for a show-off stunt.
*
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