[Guest]

Hello Forum,

Direction: "Using only the symbols +, -, x, / as replacements for the blanks, find the greatest value of expression given."

1 ___ 2 ___ 3 ____ 4 _____ 5 ______ 6 ______ 7 _______ 8

I know that subtracting and dividing make the answer smaller, but adding and multiplying make the answer bigger. So I think first I find the smaller numbers to use in subtraction and division and then save the bigger numbers for multiplication and addition.

1 x 2 + 3 - 4 + 5 / 6 x 7 x 8 = 56

Am I even close?

[Thalia]

You can get at least 60480 by adding 1 and 2 and multiplying the rest. I don't know if that is the maximum.

[curr3nt]

Are parentheses allowed?

With order of operations 1+2*3*4*5*6*7*8 = 40321 since the multiplication would take place before the addition.

[Thalia]

Point taken. Either way, 56 is not anywhere near the greatest value. So as curr3nt has put it, the highest value is greater than or equal to 40321.

@curr3nt: Any idea how to prove what the greatest value is?

[curr3nt]

Break up the equation into a smaller equation.

7*8 > 7+8 > 7/8 > 7-8

Show that for n > 1

n*(n+1) > n+(n+1) > n/(n+1) > n-(n+1)

When n = 1 then

n+(n+1) > n*(n+1) > n/(n+1) > n-(n+1)

With or without parentheses once 1+2 is done every number combination will be > 1 so the largest value will be obtained with a multiplication.

Does this logic sound right? been a long time since I did this kind of stuff.

edit - grammar/typing fail

Edited February 10, 2011 by curr3nt