The frog jumping on the lotus leaf problem

The frog sits on the leftmost lotus leaf, each step can jump to the next leaf, or one leaf away, but cannot jump back. Ask how many ways are there to jump to the last leaf, knowing that there are 10 lotus leaves in the row?

The Fibonacci sequence is a sequence of natural numbers starting with 0 and 1, then the next number in the sequence will be the sum of the previous two numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... This sequence of numbers is named after the Italian mathematician Leonardo Fibonacci, also known as Leonardo da Pisa (1170 - 1240). He is considered one of the greatest mathematicians of the Middle Ages.

The Fibonacci sequence appeared in his book "Liber Abaci" in 1202. In it, he introduced this sequence through two classic problems: the rabbit problem and the problem of the "ancestor" number of a male bee.

Nowadays, the Fibonacci sequence is widely known not only in mathematical applications, but also because it has many special properties and has wide applications in many different fields such as finance, architecture, geometry and computer science.

We won't go into this sequence in detail. If you're interested, Google "Fibonacci Sequence" or "Fibonacci Sequence" and you'll find a lot of interesting stuff related to the Fibonacci sequence.

Here we have an interesting problem related to this sequence as follows:

On the lake there are 10 lotus leaves arranged in a horizontal row. On the outermost leaf there is a frog.

At each step, the frog will either jump to the leaf next to the one it is standing on or skip that leaf to the next one. The frog never jumps backward. How many ways can the frog jump to the rightmost leaf?

>>> Answer

Vo Quoc Ba Can

Math Teacher, Achirmedes Academy, Hanoi

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