Too many Fights
John has
children from his first wife and Mary has
children from 1st husband.
John and Mary marry and have Y children.
If the family has a total of 22 children then find the maximum number of fights between the children.Assuming that children of same parents do not fight. .
The answer is 161.
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1 solution
There are three groups of children call them A, B, and C, and it is required to Maximize the number of fights which is
Fina Max of (AB + AC + BC) (1)
given that B = A + 1 and A + B + C = 22
substituting in (1), we got
A(A+1) + (A+1)(21-2A) + (A+1)(21-2A)
By differentiation w.r.t A to find the MAx
7 A = 41 ---> A = 6.833 == 7 and B = 8 and C = 7
Max no. of fights = 7 8 + 7 7 + 8*7 = 161