Question

Would appreciate it if u could explain how to solve this problem. Need to submit in 24hrs. Thanks alot.

(1) and (3) (1) and (2) 10 pts Question 11 There are nine presidential candidates (1. 2,...9) who are going to debate on TV in the evenings, each evening three candidates (a) Design a appropriate block design to group the nine candidates into triples so that any two of them meet exactly once. What are the parameters s (b) How many evenings do you need for all the debating? (c) Give a debating schedule for all the candidates according to your design. (No need to keyin here.)

Answer 1

c Schedule Block No b1 b2 b3 v-9, b-12, r-4, k-3, 2-1 3 4 In the given problem V - (1,2, 3,4,5,6,7,8,93, there are 9 vertices, thus v 9 We are asked to make (each evening three candidates) blocks having three candidates, that is 3-subsets, thus k-3 b5 b6 b7 4 Number of such blocks -b, and each candidate appears exactly r number of blocks. As the number of elements is 9, one element(candidate) can be with 8 other candidates two at a time, and hence 2 4 b8 b9 b10 9 Also any two of them meet exactly once, that is 1-1, that is, in a block two candidates can appear only once 5 b11 4 b12 (1, 4, 71, {2, 5, 8), (3, 6, 9) [1, 5, 91, f2, 4, 9), (3, 4, 8) b) As the number of blocks required to do this is 12, so b-12.

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