Posted by **Mathslover Please help** on Sunday, May 5, 2013 at 11:34pm.

A 10 km race has 5 water stations set up around the course. What is the minimum number of people that must run in the race in order to guarantee that 10 people stop at the same set of water stations?

- Math -
**DKS**, Monday, May 6, 2013 at 8:13am
289

- Math -
**hans**, Monday, May 6, 2013 at 11:14am
can u explain DKS,please...

- IIT Kharagpur -
**Nagaraju Vemuri**, Wednesday, May 8, 2013 at 1:47pm
The possible sets are 2^5 = 32.

We have one null-set.

We have 5 possible sets with one station stop(1 to 5).

we have 5c2 possible sets with two station stops etc ...

Now we can at max accommodate 9 runners per set.

If we add one more runner, some or other set will have 10 runners.

So (32 * 9) + 1 = 289 is ANSWER.

- Math -
**K**, Saturday, May 11, 2013 at 9:21am
Why the possible sets are 2^5?

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