Number 7 only 6) FBI agent X is working with 5 informants. She needs to make arr

Question

Number 7 only

6) FBI agent X is working with 5 informants. She needs to make arrangements fo the informants to communicate with each other, either directly or through others but never in groups of more than two. For reasons of security the number of meeting places must be kept as small as possible. Furthermore, each pair of informants has been assignec a danger rating (shown below) which indicates the risk involved in their being seen together. Assume the danger is proportional to the sum of the danger ratings of the individuals who meet directly. How can agent X arrange communication so as to minimize the danger ? ones Erown Hill Ritt Chen ones Brown Hill Ritt Chen 4 7) A zoo currently has 10 animals (a,b,c,d,e,f,g,h,i. and j). Each is currently kept in its own cage. We wish to have 'open space' enclosures where several animals can co-exist. The table below shows which animals are predators or prey for other animals and can not be kept together. Determine the minimum number of open space enclosures which would be required to accommodate all the animals.

Explanation / Answer

1. a and b are predators so 2 open spaces are required.

2. now e and j can't live with a but they can live with b and also e and j can live with each other so no problem there.

3. d and g can't live with b, but they can live with a so no problem there.

so far

open space 1 : a, d, g

open space 2 : b, e, j

4. c can't live with h and j. so c can be put in open space 1 and it is okay with a, d and g all.

so far

open space 1 : a, c, d, g

open space 2 : b, e, j

5. d is already in opein space 1

6. f can't live ith d and j, so it will need a separate open space

so far

open space 1 : a, c, d, g

open space 2 : b, e, j

open space 3 : f

7. g is already in open space 1

8. h can't live with c and i, so h can be put in open space 2.

so far

open space 1 : a, c, d, g

open space 2 : b, e, j, h

open space 3 : f

9. i can't live with e, h and j, so let's put it in open space 1

open space 1 : a, c, d, g, e, i

open space 2 : b, e, j, h

open space 3 : f

10. j is good to go with current placement as j can't live with a, c, f, i.

so 3 open spaces are required.

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