# Help w/ Eqn (from UK): Evaluate SX = [(E*C)+3*H-1] (A-1)[2*(G+D)-(B-2*F-1)]

#### Mike Gozna

##### New member
Hi Guys, New to this Forum. I live in UK and do a lot of Geocaching. I am working out a puzzle cache at the moment and have come up against a proplem, I am not that great at Math and was wondering if anyone can give me a heads up on the problem as follows.

The equation is:
Grid Ref: SX = [(E*C)+3*H-1] (A-1)[2*(G+D)-(B-2*F-1)]

Where A=324, B=93, C=33, D=280, E=828, F=22, G=365, H=565, and I=315.

The answer will be in the format: SX=????? ?????

I am not sure in which order to do the math, so if someone could either work it out for me, or point me in te right direction, I would be very grateful. Thank you in advance for your efforts.

#### mmm4444bot

##### Super Moderator
Staff member
… SX = [(E*C)+3*H-1] (A-1)[2*(G+D)-(B-2*F-1)]

Where A=324, B=93, C=33, D=280, E=828, F=22, G=365, H=565, and I=315.

The answer will be in the format: SX=????? ?????
I get an 11-digit number, but the middle digit is a zero.

Are you supposed to ignore the middle digit?

SX = ?????0?????

The topic is known as Order of Operations. :cool:

#### JeffM

##### Elite Member
Hi Guys, New to this Forum. I live in UK and do a lot of Geocaching. I am working out a puzzle cache at the moment and have come up against a proplem, I am not that great at Math and was wondering if anyone can give me a heads up on the problem as follows.

The equation is:
Grid Ref: SX = [(E*C)+3*H-1] (A-1)[2*(G+D)-(B-2*F-1)]

Where A=324, B=93, C=33, D=280, E=828, F=22, G=365, H=565, and I=315.

The answer will be in the format: SX=????? ?????

I am not sure in which order to do the math, so if someone could either work it out for me, or point me in te right direction, I would be very grateful. Thank you in advance for your efforts.
The formula you have given results in a single number. Of course spaces are ignored in mathematical formulas so it is possible that you mean two different numbers. If so, they should be separated by a comma.

$$\displaystyle SX = (e * c) + 3 * h - 1,\ (a - 1)\{2 * (g + d) - (b - 2 * f - 1)\}.$$

$$\displaystyle 29018,\ 401166.$$

#### mmm4444bot

##### Super Moderator
Staff member
I had considered that space as a separator, but the format for the answer shows two five-digit numbers.

#### Mike Gozna

##### New member
I get an 11-digit number, but the middle digit is a zero.

Are you supposed to ignore the middle digit?

SX = ?????0?????

The topic is known as Order of Operations. :cool:
Thanks for taking the trouble to work this out. What number have you come up with?

#### mmm4444bot

##### Super Moderator
Staff member
What number have you come up with?
You replied to my question with a question!

I would think that part of the fun of geocaching is figuring out the puzzles. So, I will guide you, and then we can compare results.

I have simplified the given expression, in parts. Each of the following parts (aka: expressions) represent a number.

E*C + 3*H - 1

A - 1

2*G + 2*D - B + 2*F + 1

The asterisks are multiplication signs.

The Order of Operations tells us that when we have an expression containing multiplication, addition and subtraction, we do all multiplications first, and then we do additions and subtractions, in order reading from left to right. I know that you can do this.

E*C + 3*H - 1

To find the value of this expression, we do the multiplications first.

Multiply number E times number C; write down the result (aka: the product).

Multiply 3 times number H; write down this product.

Now, reading from left to right, do the addition and subtraction. That is, add product E*C to product 3*H, and then subtract 1.

Call this result "factor1". Write it down.

A - 1

This expression is simple to evaluate, yes? Subtract 1 from number A. Call this result "factor2", and write it down.

2*G + 2*D - B + 2*F + 1

In this expression, each of the multiplications is simply doubling a number (2 times number G, 2 times number D, and 2 times number F). Write down these products, and then add and subtract as shown, reading from left to right. Call the result "factor3".

Now multiply factor1 times factor2 times factor3, and show us what you get.

Cheers

#### stapel

##### Super Moderator
Staff member
The equation is:

Grid Ref: SX = [(E*C)+3*H-1] (A-1)[2*(G+D)-(B-2*F-1)]

Where A=324, B=93, C=33, D=280, E=828, F=22, G=365, H=565, and I=315.
You've been given values for the letters. Plug the numbers in for the letters, and do the arithmetic. It's just subtraction (the "-" sign), addition (the "+" sign), and multiplication (the "*" sign). Where are you getting stuck?

For instance, you plugged $$\displaystyle (828)\times(33)$$ into your calculator, and got... what? You plugged $$\displaystyle (3)\times(565)$$ into your calculator, and got... what? You added these two numbers, and subtracted the 1, and got... what?