SOLUTION: The values of a,b,c, and d are 1,2,3 and 4, though not necessarily in that order. What is the greatest possible value of ab+bc+cd+da?

Question 978646: The values of a,b,c, and d are 1,2,3 and 4, though not necessarily in that order. What is the greatest possible value of ab+bc+cd+da?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
looks like it's 25.
i used excel to generate all possible combinations and it appears there are several combinations that would get you the maximum value of 25.
a logical approach might be as follows:
4*3 = 12 is the highest possible combination.
4*2 = 8 is the next highest possible combination.
3*2 = 6 is the next highest possible combination.
a combination that give syou this would be:
a = 3
b = 1
c = 2
d = 4
you will get:
3*1 + 1*2 + 2*4 + 4*3 which results in:
3 + 2 + 8 + 12 which results in:
25.
one other combination that i found (there are several) that also gets you 25 is:
a = 1
b = 3
c = 4
d = 2
you will get:
1*3 + 3*4 + 4*2 + 2*1 which results in:
3 + 12 + 8 + 2 which results in:
25
all winning combination have 8 and 12 in them which is the reuslt of 3*4 and 2*4.
none of them have 6 in them which is the result of 3*2.
apparently it's not possible to get 3*2 and 2*4 and 3*4 in the same combination.
bottom line:
maximum value is 25.

RELATED QUESTIONS
the values of a, b, c, and d are 1, 2, 3, and 4, but not necessarily in that order. what... (answered by checkley71)

the values of a, b, c, and d are 1, 2, 3, and 4, but necessarily in that order. what is... (answered by venugopalramana)

The values of a, b, c, and d are 0, 1, 2, and 3, although not necessarily in that order.... (answered by Edwin McCravy)

Five points, A, B, C, D, and E, lie on a line, not necessarily in that order. segment AB... (answered by Fombitz)

each of the integers 1,2,3, and 4 is represented by one of the letters A,B,D and M, not... (answered by Edwin McCravy)

Okay, I am taking Algebra again after a 10 year lapse. The following question is really... (answered by edjones)

If {{{ab^2c^4=2430000}}}, where a, b and c are distinct positive integers greater than 1, (answered by greenestamps,ikleyn)

in the expression w/x - y/z = 1 the letters can be replaced by the numbers (1,2,3,4) but... (answered by Theo)

in the expression w/x - y/z = 1 the letters can be replaced by the numbers (1,2,3,4) but... (answered by checkley77)