Like Digits
this is a puzzle with instructions. There are no hidden hints or
clues. Find an elegant way to solve it, and you won't need any
programming or a spreadsheet, maybe just a calculator (*).
On an analog clock with 3 hands (hours, minutes,
seconds), the 3 hands overlap exactly only once every 12 hours, at
noon and midnight. In between, those 3 hands have several
near misses, but never overlap perfectly. Find the exact time, in
hours, minutes, seconds and 1000ths of a second, when the 3 hands
have the closest near miss (excluding anything within 5 minutes
before and after noon/midnight, which isn't a near miss). Define
the closeness as the size of the inside angle between the hands at
any time. You are looking for the time when the largest of the 3
inside angles formed by the 3 hands (h & m, h & s and m
& s) is the smallest. You should find 2 solutions with the
exact same angle.
Use the earliest solution, T1, to calculate
the coordinates of the cache:
T1 = A hours, B minutes, C
seconds and D/1000ths of a second
(hours go from 0 to 11, minutes and seconds go
from 0 to 59)
N = [((A * B) + 11) * D] + (C -5)
W = (C - 2) * D + (2 * A * B) + 1
The cache is located at:
North 37º nn.nnn (where nn.nnn = N/1000)
West 122º ww.www (where ww.www =
W/1000)
Use the latest solution, T2, to get a
location hint:
T2 = E hours, F minutes,
G seconds and H/1000ths of a second
(hours go from 0 to 11, minutes and seconds go
from 0 to 59)
X = (2 * E * F) - (H + G)
Y= (F + E + E + 4)/G
Cache is located X ft high, facing Y
"hours" true north.
The cache can be found with the coordinates only.
But it will be harder. The cache is slightly larger than a micro,
but does only contain the log sheet and stash note. Bring your own
pen.
(*) if you'd like to receive the
elegant solution after your find, email me your final coordinates
and I'll reply with the elegant solution.