Superman's hurdle race

Superman is taking part in a hurdle race with 12 hurdles. At any stage he can jump across any number of hurdles lying ahead. For example, he can cross all 12 hurdles in one jump or he can cross 7 hurdles in the first jump, 1 in the later and the rest in the third jump. In how many different ways can superman complete the race?

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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Comments

You are discussing questions from the BdMO (Bangladesh Math Olympiad) -2012, aren't you?

Mursalin Habib - 8 years ago

All of the 3 discussions are from MO question sets...

I tried to utilize Brilliant !!!!!

Sheikh Asif Imran Shouborno - 8 years ago

We solve this recursively.

Let $f(n)$ be the number of ways Superman can complete a race with $n$ hurdles. Clearly, $f(n)=\displaystyle \sum_{i=0}^{n-1} f(i)$ . And since we have $f(0)=f(1)=1$ , it's not difficult to see that $f(n)$ is in fact $2^{n-1}$ .

Mursalin Habib - 5 years 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}`	$\boxed{123}$