No, not that kind of sign...

Right then. Assume you’re using a basic calculator and you press the numbers in the order shown, replacing each question mark with a mathematical sign. Add, subtract, multiply and divide can each be used only once. What’s the highest number you can possibly get?

**5 ? 4 ? 7 ? 3 ? 2**

Good luck!

Vel.

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May 10, 2010 at 5:14 pm

On a basic calculator, order of operations is ignored. So, we can say that this problem is the same as (((5 A 4) B 7) C 3) D 2, where A,B,C,D are members of S={+,-,*,/} and all have unique values; the members of S have their standard meanings in the algebra of the reals.

In order to maximize the result, the division must be done by as small a number as possible. So, D must be /.

We want the subtraction to be by the second smallest number. So, C must be -.

We want the multiplication to be between numbers that are as large as possible. So, B is * and A is +.

(((5+4)*7)-3)/2)=(63-3)/2=30.

I thought about writing a program to brute force all the solutions and check my answer, but meh, I’m feeling lazy. Hopefully someone else will do such a thing or something similar.

If I end up doing it myself later, I’ll post the code and my results.

May 10, 2010 at 8:11 pm

I think you’ll find that, with these four operators and your logic (division by smallest number, multiplication by largest, etc), you’ll always get the biggest number possible, so you probably don’t need to double check it.

May 10, 2010 at 8:36 pm

I tried a few other combinations after being lucky on the first attempt – closest I got was about 5 lower so am agreeing with Xbalanque on the answer, not on the method used to discover it!! 😀

Sorry, Xbal!

May 11, 2010 at 5:37 pm

I pretty much used the same logic as Xbal, only not as formal. And it was my first ‘guess’ too! So I got 30 as well.

(It is helpful when I find the more current puzzle, no? XD)

May 11, 2010 at 9:34 pm

Ditto, I got 30 too. Using the same logic as Xbal.. but I didnt bother with formulas etc

May 14, 2010 at 6:45 pm

Heh, the only reason my stuff is a bit more formal, is one of my majors was math. Even though I did a lot of Applied electives, I was actually in the “Traditional” (“pure”) track, so I got very used to just writing proofs off the top of my head.

So, when I’m presented with a problem that requires me to think that way, well, that’s how I’ll tend to express it. I suppose if I had taken an additional pass at my comment before posting, I might have trimmed some of the unnecessary formalities and information, but meh.