4. The Interstellar Surfing Association (ISA) is having its annual meeting to de

Question

4. The Interstellar Surfing Association (ISA) is having its annual meeting to determine the rules for this year's Interstellar Surfing League competition. Alex, the new overlord of the ISA, is insisting on a new rule: Each competition must be held at a different location, and no two competitors may participate in the exact same set of competitions. This means that for any two surfers, their lists of locations where they have competed must differ by at least one entry. Naturally, it is required that all surfers must compete in at least one competition. You must fully justify your answers to the following questions. (a) If there are 300 surfers signed up for the Interstellar Surfing League, what is the smallest number of locations that must be reserved for surfing competitions, so that the new rules are met? (b) In general, with n different possible surfing locations reserved for competitions (after al, one cannot reserve all the beaches in the galaxy), what is the maximum number of surfers that can compete so the new rules are still met?

Explanation / Answer

Solution:

According to the question here we have two rules are given.

1. ) 2 competitions may not be paticipate in the exact same set of competitions.

2.) Each competitions must be held at different locations.

Then,

a) If there are 300 surfaces so the smallest number of locations must be

300/2 = 150, so each two players can play at one location.

Hence the minimum number of locations is 150.

b)Now, if we have 'n' number of location to the maximim number of surfaces must be '2n' who can compete the maximum number according to the rules or conditions given.

Thanks

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