A New Angle on the Legend of Cocaine Island
The Mystery
When choosing a vacation spot, my friends and I really only look for three things: beaches, pina coladas, and no schedule. In other words, we are looking for the island paradise of Culebra, Puerto Rico. As one local put it, “In Culebra, mañana doesn’t mean tomorrow, it just means not today.” But don’t mistake its lax island vibes for it being uninteresting. After being discovered by Christopher Columbus in 1493, Culebra was a refuge for pirates until the 19th century, a US Navy camp from 1901–1975, and the rumored home to a still-lost $2 million stash of cocaine. Culebra is chock-full of mysteries, and we were about to discover one more.
We were a few hours into enjoying the Caribbean sun, blue waters, and white sand on Culebra’s Zoni Beach when my friend, Roman, rushed over to me holding a rusted tin coffee can. He found it just a few feet into the brush while answering “nature’s call”. Inside the tin can was a typed note — no special formatting, no signatures, just the cryptic words:
“All are uncovered over the water. 1.2 miles northeast, 50 feet from the post. Buried 4 feet for safekeeping.”
I could barely keep it together — this is the stuff of movies, and now I’m living it! Unfortunately, the note didn’t make a whole lot of sense, but it seemed like it was giving rough directions to something buried. We had no idea if there was any significance to the tin can’s location when Roman found it. For all we knew, the tin can was washed up during a storm or a tourist from New York dropped it.
But what if someone purposefully placed the note at that spot on Zoni Beach? Could we be within a couple miles of buried treasure from Columbus, pirates, or drug dealers?
We reasoned that if the note was placed at that specific spot, then “1.2 miles northeast” would point to some interesting location on Culebra. From there, we could figure out the more specific “50 feet from the post” and “buried 4 feet.”
But as we looked northeast, all we saw was blue water and the small, uninhabited island of Cayo Norte (pictured above). Our hearts initially sank, but then we thought that hiding the treasure on an island would fit with the note’s phrase, “over the water.” Could Cayo Norte be home to the buried treasure?
The Disagreement
Looking over the water at Cayo Norte, I was sure it was at least three miles away. But another friend was sure it was only half a mile, and the others were somewhere in between. Continuing the treasure hunt depended on figuring out the distance to the island, but how can we, with no cell signal, actually calculate the distance?
Enter trigonometry.
We reasoned that if we can form a triangle with two points on our beach and the third point on Cayo Norte, we can use trigonometry to solve all the triangle’s angles and side lengths with only a few measurements from our beach. By doing so, we find our distance to Cayo Norte. If the distance is roughly 1.2 miles as described in the note, then there is a good chance it could be the home to buried treasure!
Making the Measurements
As depicted in Figure 1 (middle), we labeled point B as the location of our beach chairs and point A some arbitrary distance down the beach. We agreed to label point C as the lowest saddle point amongst Cayo Norte’s rocky hills. We chose some driftwood as a straightedge to carve the three sides of the triangle in the sand from points A and B (see Figure 1, left and right).
Next, we made three measurements: (1) the angle θA (Figure 1, left), (2) the angle θB (Figure 1, right), and (3) the side SC, the distance between points A and B. To measure the two angles, we took a photo of the lines carved into the sand and used our phone’s built-in photo cropper to find the angle. We determined the length of side SC by multiplying the number of steps between points A and B by our estimated stride length.
We measured:
θA = 99°
θB = 73°
SC = 268.5 meters (~0.167 miles)
Solving the Triangle
With these three measurements, we could now solve the entire triangle! Since the angles of a triangle add to 180 degrees, we know the angle θC=180-θA-θB. Then we used the Law of Sines to find the two missing side lengths.
Specifically, to find side SB, the desired distance between our beach chairs and Cayo Norte, we calculated
To complete the triangle, we similarly found side SA:
We plugged our measurements into the equations to find:
θC = 8°
SA = 1,906 meters (~1.18 miles) *our measurement of interest*
SB = 1,845 meters (~1.15 miles)
We determined that the distance between us (point B) and Cayo Norte (point C) is approximately 1,906 meters, or 1.18 miles!
Is There Buried Treasure on Cayo Norte?
Ok, so 1.18 miles is pretty darn close to the note’s 1.2 miles! It took all the restraint we had to not swim out to the island and start poking around. When we went back to our Airbnb with internet connection, we used Google Maps to confirm true distance of 1,810 meters, or 1.12 miles. We were pretty impressed with our spontaneous treasure hunting skills, using just sticks, sand, and math to get a pretty decent distance measurement.
While point C specifically is 1.12 miles away, many locations on Cayo Norte would satisfy the “1.2 miles” condition described in the mysterious note. The next step is to go to the Cayo Norte itself and figure out if there is an obvious “post” — maybe a fence post or old military post — that fits the note.
Unfortunately, of the three large keys off of Culebra — Culebrita, Cayo Luis Peña, and Cayo Norte — Cayo Norte is privately owned and not accessible to tourists.
If there is buried treasure on Cayo Norte, what could it be? Since the note was typed in English and packaged in a modern-era tin coffee can, it is most likely not describing any treasure dating back to Christopher Columbus or pirates. Or the US Navy found long-lost pirate treasure and reburied it? Or maybe we are one step closer to solving The Legend of Cocaine Island?
This mystery looks unlikely to be solved today, but who knows, maybe it will be solved mañana.
Note: You can read the true, but more boring, version of this story in the article titled, “Settling Disagreements with Trigonometry: Don’t Take Sides, Solve Them.”
