# steiner triple system in design theory

*label*Mathematics

*timer*Asked: Dec 10th, 2017

*account_balance_wallet*$5

**Question description**

I need the solution for this problem

the problem about steiner triple system in design theory

I need it within 2 days with no extended time

## Tutor Answer

I did it before bidding:)

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(πβ1)

triple containing them. The quantity of these pairs is ( ) = 2 .

2

π(πβ1)

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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