# Treasure hunt 'round the world! (clue 2)

If you're interested in starting the treasure hunt from the very beginning, check out the prologue!

Upon arrival at the Pamplona Airport, you head towards baggage claim. Standing at baggage claim, you see a man in a suit and sunglasses. One hand is behind his back; in the other, he holds a sign that reads "[insert username here]". Walking up to him, you say:

"Hi. My name is [insert username here]. Do you have something for me?"

Without hesitation, he stretches the arm from behind his back out towards you. In it he holds a small envelope. You take the envelope and eagerly tear it open, pulling another small card out from inside. The card reads:

Congratulations on your arrival in Pamplona! I'd suggest you stay and enjoy the city (it is a beautiful city), but there's no time for that - you're running a race! Grab your bag, rent a car, and hit the road! This time, you're driving to your next location, which is (more or less) detailed on the back of this letter.

Yours truly,

Bailey M
Puzzlemaster for the Treasure Hunt 'Round the World

You flip over the letter and read:

Lisbon, Portugal: 7.3498737047383369
Knockainey, Ireland: 7.2723983925700463
Boudekak, Algeria: 6.8394764382288426

As you circle in on the answer, make careful note of your location. At some point down the line, you'll be left with two. Don't look too closely here, as your first instinct will most likely be correct. Once you've centered in on the solution, the final destination (much like the above numbers) should feel natural.

As you finish reading, you notice your suitcase drop onto the conveyor belt. Time to grab that bag and hit the road!

The story continues in the next part, Treasure hunt 'round the world! (Interlude 1)

• Does the final destination also has a number associated with it? Or are the numbers only used to work out the final destination?
– Eli
Jun 30, 2015 at 7:15
• The numbers are just part of the puzzle. The answer won't have a specific number attached to it. Jun 30, 2015 at 13:43
• Maybe find the point where circles around each of these three destinations intersect? Or draw a circle connecting these three destinations and find the centre of it? (Would that be the same place either way?) Jun 30, 2015 at 15:50
• Wonderful puzzle as always @BaileyM! Jun 30, 2015 at 20:16

The final destination is:

Definitely throw PrincessTrevor a +1 for posting the logarithm portion first.

The portion of the letter that says:

the final destination (much like the above numbers) should feel natural.

implies that the numbers listed above are natural logarithms. These numbers correspond to:

Lisbon, Portugal 1556
Knockainey, Ireland 1440
Boudekak, Algeria 934


Some other portions of the letter:

As you circle in on the answer

implies that we should be looking for circles.

Drawing circles on the map with the radius listed above and at the locations in Google maps gives this image:

At some point down the line, you'll be left with two

is referring to, Toledo, Spain and Turin, Italy because they lie at the intersection of two of the circles and is inside the third.

At some point down the line, you'll be left with two. Don't look too closely here, as your first instinct will most likely be correct. Once you've centered in on the solution, the final destination

The final destination lies halfway on a line between Toledo and Turin.

Once you've centered in on the solution, the final destination (much like the above numbers) should feel natural.

The final destination:

Parc Natural de la Vall de Sorteny is pretty "natural"

• Toledo and Turin are the two you're left with! However, neither are the final destination. You're very close to finding it. :) Jun 30, 2015 at 18:41
• Of course! I figured it out when I posted this. Jun 30, 2015 at 18:43
• @BaileyM I'm confident with what I've put so far, but the final leap I'm not quite as confident with. I feel like there are too many places possible on the final line. I'm afraid that no matter which choice I make I'm guessing. Maybe I'll just have to leave it for a bit. It's such a tease ;) Jun 30, 2015 at 19:20
• You're SO close! The answer is more specific than you're looking. You might need to zoom in on whatever map you happen to be using. Jun 30, 2015 at 19:27
• I also need to figure out the google API for lines now. Took me a bit to figure out circles :) Jun 30, 2015 at 19:29

Based on what I've found so far, I'd go with

Boudekak, Algeria

Using the line, "the final destination (much like the above numbers) should feel natural.",

I decided to work with natural logarithms.

So,

Taking the natural log of each of the numbers given isn't terribly helpful so far as I can tell (yielding 1.994, 1.984, and 1.922 respectively). So, instead, I did the reverse and squared e by the numbers given. This gives 1554, 1438, and 933 for each number.

And here's what makes it fit, for me:

Looking up the distance between the locations "as the crow flies" from Pamplona to the given locations gives:
1) 779 Kilometers for Lisbon, Portugal
2) 1186 for Knockainey, Ireland
3) And finally, 932 for Boudekak, Algeria
Seeing as there was probably a bit of rounding that happened here, I think that difference of 1 is close enough to call that good.

• You're on the right track, for sure. To help you a bit, the final destination is not one of the three cities listed. Also your numbers are all either 1 or 2 lower than my intended numbers, but that shouldn't affect the solution. Jun 30, 2015 at 17:48