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Leap frog addition

Leap frog addition

This mathematical trick follows the property of Fibonacci series. You can play this simple trick with your family and friends. Take a card with 10 blank lines. Fill any number from 1 to 20 in the first two lines. Write the sum of previous two lines for the successive lines.

The sum of the first two line will be written in the 3rd line, in the same way sum of the 2nd and 3rd line will be written in the fourth line. Repeat the process till the 10th line. Total all the numbers. But you can easily reveal the total much faster than your friend, because the answer will always be 11times multiples of 7th number.

Let us try this with an example,

1. 3

2. 4

3. 7

4. 11

5. 18

6. 29

7. 47

8. 76

9. 123

10. 199

Answer is 517.(which is 11 times 47)

To find quotient divide the line 10 by line 9. The answer will be always 1.61 (2 decimal places). More remarkable fact about the leap frog addition is, if the addition is continued with many lines, then the successive ratio will end with the golden ratio 1.6180339... Leap frog addition can be written as two dimensional linear system of equations.

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