+0

0
307
2
+1825

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 ?

tertre  Jun 1, 2017
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#1
+83935
+1

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???

CPhill  Jun 1, 2017
edited by CPhill  Jun 1, 2017
edited by CPhill  Jun 1, 2017
#2
+1825
+1

It's correct!

tertre  Jun 2, 2017

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