The cache is not at the published coordinates.
As the sun began to set under the sand dunes, two explorers were finishing an arduous journey atop mighty camels. They had been travelling for several weeks to the heart of a long lost city, which was built around an oasis. Their shadows were cast far over the parched ground, all the way to the illusory haze near the horizon. At their destination, they dismounted by the water and moved through the ruins to the entrance of a crypt, which had been built into the nearby cliffs, with a sphinx statue on either side. They ventured inside to learn as much as they could about the ancient civilisation that once resided here.
Within the catacombs, the explorers encountered a heavy, ornate door that could only be opened by a mechanism that was tied to a puzzle that had to be solved. There were 12 circles written on the wall, each of which was subdivided into a varying number of segments, a portion of which were shaded a different colour. Each circle had two or three panels to the right of it. These panels contained complex rotary mechanisms that allowed ancient Egyptian number symbols on it to be manipulated to allow the representation of any natural number less than 10,000.
It appeared that an explorer had been here before, because scrawled above each of the circles in white chalk was the fraction it represented. Also, the panels next to the first six circles already had their numbers set, although it seems that the explorers never finished the remaining six circles for reasons unknown. Following is each of the fractions with the value of each of its panels next to it:
\(3 \over 5\): 2, 10
\(2 \over 13\): 7, 91
\(11 \over 24\): 3, 8
\(8 \over 9\): 2, 3, 18
\(9 \over 29\): 6, 7, 1218
\(17 \over 25\): 2, 6, 75
\(9 \over 10\): a, b, c
\(10 \over 21\): d, e
\(4 \over 9\): f, g
\(13 \over 16\): h, i, j
\(13 \over 40\): k, l
\(2 \over 7\): m, n
Can our explorers work out which numbers to set the remaining 14 panels to? Can you?
There is only one solution to each of these fractions with the given number of panels. I've checked using a computer with a brute force search.
The real coordinates are: N 54° 17.opq W 000° 24.rst
o = c / b + a + 1
p = e - d
q = g / f
r = j / i + h
s = l - k - 1
t = n / (m + 3) - 3
I have chosen an area with a view of a place that I thought looked fitting for the theme of this cache (no photos though, please!).
As with any puzzle of mine, feel free to message me if you want help with any aspect of this puzzle.
Congratulations to marions27 for FTF.
Last cache check: 11 July 2025