# Need help with problem related to latitude and longitude coordinates

My husband's boss is taking all the sales team to a team building event in Denver, Colorado and he has been sending hints for the last week. Now he has sent a math problem and told us it has something to do with Latitude and longitude. I have worked on this problem for days. If you could help that would be wonderful. Thanks in advance.

Here is the problem: \begin{align}13&+(-459.67)+(45-45-90)+14.0067(2)\\ &+1,000(2)+10^9+(-459.67)\\ &+(100^2 \times 2)+((101)^2)^2\end{align}

The bossman said it doesn't necessarily have to do with just the answer. Please someone put me out of my misery! ha!

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I'm sorry I guess the math problem can be broke down into latitude and longitude coordinates and I was just wondering if anyone else is able to figure out how. – Stephanie Jul 10 '12 at 19:10
Is the "$2\times 2$" supposed to be in parentheses, perhaps? – Cameron Buie Jul 10 '12 at 19:12
I guess that the boss said to dissect the problem and it should be apparent what it is about but I have dissected this problem like crazy. – Stephanie Jul 10 '12 at 19:13
Also, what does "it doesn't necessarily have to do with just the answer" mean? What is the "it", here? Also, the answer to what? The "problem" is just an expression--nothing has been asked, so far as I can tell. Do the hints he's been sending have anything to do with the problem, perhaps? If you post those, too, it might be easier for someone to see how to break it down. – Cameron Buie Jul 10 '12 at 19:16
It looks like it's just a matter of calculating a number. The issue is that there doesn't seem to be a "problem" here to solve really, just a calculation to carry out. I would assume that 1000(2) is $1000^2$, but then you use ^ in other places so I don't know if that's right. Also your $10^9$ and $101^4$ terms will completely drown out everything else, and I don't know of anything in geography where you'd deal with numbers that large. Lots of redundant brackets. The whole thing just looks weird. Some legs may be being pulled here. – Robert Mastragostino Jul 10 '12 at 19:18

Edit: Based on your edit, the expression, itself, evaluates to: $$1,104,081,432.6734$$

Your comment hints give me a few ideas:

(i) $13$ is a prime number. Perhaps a reference to the prime meridian as a starting point?

(ii) $-459.67$ is an approximation to absolute zero ($0$ Kelvins) in degrees Fahrenheit.

(iii) $45$-$45$-$90$ is how one often indicates the angles of a right isosceles triangle.

(iv) $14.0067$ is the atomic mass of Nitrogen. Pure Nitrogen is found in nature as a molecule $N_2$ (two nitrogen atoms bonded together). This may be connected to the $(2)$ appended to the end of the $14.0067$.

I'm not sure what to think about the rest of it. Hopefully this gives you some clues....

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I like your idea of taking the "calculation" apart. I might replace the -459.67 with OK or OR (0 Kelvin or Rankine). The powers of 10 might become K or M for 1000, B for 10^9. Nothing comes to this math person's mind about 13 except prime or maybe king (rank in deck of cards). – Ross Millikan Jul 10 '12 at 22:17
Using the hint that this has to do with latitude and longitude, we might parse this as follows: 13 -> prime (meridian) – Rick Decker Jul 11 '12 at 1:16
Oops! Spent more than five minutes writing my comment. Here's the rest. Using the hint that this has to do with latitude and longitude, we might parse this as follows: 13 -> prime (meridian) (45-45-90) -> north and west coordinates -459.67 -> zero degrees Then the last term, $((101)^2)^2$ could be interpreted as $101^4=104060401$, which is a scaled version of 104, fairly close to the west longitude of Denver. Because of the two zero degree terms, it's reasonable to expect that it somehow gives the N and W coordinates of some location, but it's not clear right now. – Rick Decker Jul 11 '12 at 1:28
Here is the posers other hints. LOL – Stephanie Jul 11 '12 at 13:52
Where are the other hints? – Cameron Buie Jul 11 '12 at 13:57

This is mostly based on @Cameron's hints, doesn't quite match the problem in it's current form, and doesn't have to do with latitude or longitude. But:

• 13 = M
• -459.67 = O
• 45-45-90 = V
• ? = I
• 14.0067 = N
• 1000 = G
• $10^9$ = T
• -459.67 = O
• $100^2\times 7 + 101^2$ = 80201

Alternatively, my first thought was the triangle might be for I and there might be an interpretation of 13 as G.

I was trying to coerce a Denver zip code, but $100^2\times 2 + 101^2\times 2=40402$ or $100^2\times 6 + 101^2\times 2=80402$ work for Annville, KY and Golden, CO, too.

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I don't get where the $T$ is coming from. – Cameron Buie Jul 11 '12 at 13:56

If you just feed it to Wolfram Alpha, 1.1040823519434 × 10^9 comes back. This is 1,104,082,351.9434 when not in scientific notation. This assumes the (2)s are to be multipliers, not squares. Usually latitude/longitude in the US has fifteen digits, DD MM.MMM in latitude first, followed by DDD MM.MMM in longitude (at least the geocachers use this). This doesn't fit that pattern. Google uses DD.DDDD DDD.DDDD, which is one digit short. I can find 104.9434 embedded, which is a nice latitude in Denver, but can't find a reasonable latitude from what is left.

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Looks like she had a typo in the original post. See if that changes anything. – Cameron Buie Jul 10 '12 at 21:24