# Math

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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 -

289

• Math -

• IIT Kharagpur -

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 -

Why the possible sets are 2^5?

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