# steiner triple system in design theory

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the problem about steiner triple system in design theory

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Borys S
School: UT Austin

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We have π red points, π blue points and some quantity of triples, each of them containing
2π + π or 2π + π. Also we know that each two distinct point are contained in exactly one
triple.
(a) how many triples of the 2π + π type? For each pair of distinct π points there is only one
π
π(πβ1)
triple containing them. The quantity of these pairs is ( ) = 2 .
2
π(πβ1)
π
(b) the same way the quantity of 2π + π triples is ( ) = 2 , i.e. there are
2
π(π β 1) + π(π β 1)
2
triples at all.

From the other hand, each two points among all π + π have exactly one triple. This way...

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Anonymous
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