Frog on lotus leaves

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$n(>1)$ lotus leaves are arranged in a circle.A frog jumps from a particular leaf by the following rule:It always moves counter clockwise.From starting point it skips one leaf and jumps to the next.Then it skips 2 leaves and jumps to the following.That is in $3$ rd jump it skips $3$ leaves and in the $4$ th jump it skips $4$ leaves and so on.In this manner it keeps moving round and round the circle of leaves.It may go to one leaf more than once.If it reaches each leaf at least once,then prove that $n$ (The number of leaves) cannot be odd.

$\textbf{Note:}$ A similar problem came in the entrance examination of the Indian Statistical Institute this year.

#NumberTheory #ModularArithmetic #Sequences #Goldbach'sConjurersGroup #IntroduceYourself

Easy Math Editor

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Comments

Not just a similar problem, the same problem.

A Brilliant Member - 7 years ago

I think they asked for somd minimum valurpe right? Thats why I said similar...

Eddie The Head - 7 years ago

Let no. Of leaves which frog jumped is x therefore no.of leaves left is equal to x(x+1)/2.so total no of leaves is x(x+3)/2...... This is where i reached if nyone canfurtur solve please help

Pratyush Khandelwal - 7 years ago

Brennan Baller - 4 years, 6 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$