+4609 The values of f, g,h and j are 5, 6, 7 and 8, but not necessarily in that order. What is the largest possible value of the sum of the four products fg,gh , hj and fj ?
+128475
Line them up like this
f g h j fg + gh + hj + fj
8 7 6 5 = 56 + 42 + 30 + 40 = 168
8 7 5 6 = 56 + 35 + 30 + 48 = 169
8 6 7 5 = 48 + 42 + 35 + 40 = 165
8 6 5 7 = 48 + 30 + 35 + 56 = 169
8 5 6 7 = 40 + 30 + 42 + 56 = 168
8 5 7 6 = 40 + 35 + 42 + 48 = 165
7 8 6 5 = 56 + 48 + 30 + 35 = 169
7 8 5 6 = 56 + 40 + 30 + 42 = 168
7 6 8 5 = 42 + 48 + 40 + 35 = 165
7 6 5 8 = 42 + 30 + 40 + 56 = 168
7 5 8 6 = 35 + 40 + 48 + 42 = 165
7 5 6 8 = 35 + 30 + 48 + 56 = 169
It appears that no matter the arrangement, we will end up with 4 sets of the following sums
165, 165, 168, 168, 169, 169
So.....the arrangement that generates the max sum appears to be 8*7 + 7*5 + 5*6 + 6*8
And a possible max sum is produced when f = 7, g = 5, h = 6 , j = 8
Note that other assignments are also possible
P.S. - could someone else verify this???
