JMO Question!

An odd number of sticks lie along a straight line in a particular type of game, the distance between consecutive sticks being 10 meters. The sticks are to be collected at the place where the middle stick lies. A player can pick only one stick at a time. He has to start picking the sticks from extreme end of one side. If total distance covered by the player is 3km, find how many sticks would have been used in the game.

#JMO #ArithematicProgressions

Easy Math Editor

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`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`	$\sum_{i=1}^3$
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`\boxed{123}`	$\boxed{123}$

Comments

its easy one the answer is 25.

Yash Kumar - 5 years, 9 months ago

How so?? Can you post a detailed solution??

Vaibhav Kandwal - 5 years, 9 months ago

Let's represent the middle stick as $a_0$ . Note that the distance to be traveled for $(a_n)^{th}$ stick is equal to the distance to be traveled for $(a_{-n})^{th}$ stick. So, $1500$ meters were traveled to collect $n$ sticks in an arithmetic progression with $a = 20$ , $d=20$ .

Vishnu Bhagyanath - 5 years, 9 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}`	$\boxed{123}$