Question

can i get an explenation on how to solve this , i forgot the formula so a solution with the formula would be appreciated

For the following values of (v, k, r) either construct a design on v points, blocks of size k and each point in r blocks, or explain why such a design cannot exist. (i) (v, k, r) = (9, 3, 4). (ii) (v, k, r) = (9, 6, 8).

Answer 1

We know that

bk = vr      ...(1)

where b is the number of blocks which can not exist in decimal.

Also

     ...(2)

where is th number of blocks containing any 2 specific points, which again cant exist in decimal

(i) (v,k,r) = (9,3,4)

Verifying if equation (1) is valid in this case

bk = vr

b *3 = 9 *4

b = 12

which is valid

now verifying equation (2)

* 8 = 4 * 2

= 8/8 = 1

Thus such a design can be constructed

(ii) (v,k,r) = (9,6,8)

Verifyinf the (1) equation

bk = vr

b * 6 = 9 * 8 = 72

b = 12

verifying (2)

* 8 = 8 * 5

= 5
Thus this design can be constructed as well.