BrilliantBeard’s Buried Treasure

The sequence “WLV” appears $6$ times at the $40^{\text{th}}$ , $201^{\text{st}}$ , $222^{\text{nd}}$ , $243^{\text{rd}}$ , $271^{\text{st}}$ , and $278^{\text{th}}$ position.

The last two positions suggest that the keyword is $278 - 271 = 7$ letters long and this is confirmed by the fact that any two positions have a difference of a multiple of $7$ .

The whole code is $385$ letters long. A keyword that is $7$ letters long will divide the message up into $\frac{385}{7} = 55$ letters long. The expected letter frequency for $55$ letters in the English language is as follows, where blue shows the most frequent letters and red shows the least frequent letters:

Starting with the first letter D and every seventh letter after this, we have the letters DJWJTIHCDKDPTSJPAARCHSNGGTNLGRPHCPPEGXIGKIEPEATGIPXGRQC, which has letter counts of:

Sliding the expected letter count list until the reds and blues (mostly) line up with the seventh letter list suggests that P decodes to A, so the first letter in the keyword is P.

Repeating this process for the second letter and every seventh letter after this suggests that the second letter in the keyword is L:

the third letter is U:

the fourth letter is N:

the fifth letter is D:

the sixth letter is E:

and the seventh letter is R:

which makes the keyword “PLUNDER”.

The message can then be decoded to:

or with punctuation:

“On the fourteenth day of our journey, we spotted the southern slopes of Viete Volcano on Pi Island, sailed towards Bernoulli Bay, and made landfall at Poincare Point. I then selected five loyal men from the crew and we journeyed eastwards across the Cartesian Plains and then southwards towards the Pythagorean Peninsula. It was there at the very southern tip of Pythagorean Peninsula between two large palm trees that we buried our treasure. - Captain BrilliantBeard.”

Therefore, the treasure is buried on the southern tip of Pythagorean Peninsula, which corresponds with the number $\boxed{24}$ on the map provided.

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When you finally arrived on Pi Island to claim the treasure, you were able to dig up a large wooden chest. However, upon opening it, you were disappointed to only find some old parrot bones and a note which said, “Here lies ‘Treasure’, my beloved pet parrot. I employ a more secure encryption method for my buried gold, as any landlubber can crack a Vigenere cipher! - Captain BrilliantBeard.”