I devised and set “Possible Prime Provides Problematic Puzzle” (GC7Y78T) intending it to be a very difficult puzzle. I was, therefore, amazed when somebody solved the puzzle within 6 hours, and there was a FTF from a second solver only 12 hours after the cache was published!
Unfortunately, I had made a couple of foolish errors that allowed the cache to be located fairly easily. One method involved a short cut to finding the factors, the other way simply required some lateral thinking.
The history of failed ciphers is littered with ‘lazy’ operators and ‘clever strategies’ that, whilst supposedly making the cipher more complex, actually introduced weaknesses that could be exploited by the code-breakers.
Perhaps the most famous of these weaknesses was in a refinement to Germany’s Enigma coding machine in the Second World War. The original machine had three rotors which, each in turn, scrambled the letter fed into it, yielding millions of possibilities, and changing the combinations after each letter. An early refinement to the machine put a “reflector” at the end of the three rotors so the letter was passed back along the chain of rotors one more time, scrambling each letter a total of six times, instead of three. The code-makers believed this would make the enigma code even more secure, even unbreakable. Unfortunately, they failed to realise a simple flaw. Doing this meant that, due to the design of the machine, a letter could never be encoded back to itself. i.e. an ‘A’ could be encoded to any letter *except* ‘A’. This allowed the code-breakers to target fragments of the message with phrases that they believed were in the message. (Contrary to what was shown in a popular film, the most commonly targeted phrases were weather based, ‘wind speed’, ‘visibility’ etc, not “Heil Hitler”). This weakness is what ultimately led to the breaking of the Enigma Code.
This puzzle doesn’t, I hope, succumb to any such weaknesses and should prove *very* hard to solve.
The task is simply stated. Just find the two factors1 of the rather large number below. Then extract from the factors the digits indicated to find the coordinates.
The number is:
54619522885803207472214374630191243250590849559339
87313709409159333733922178639669681109522620819283
87187445018397691110142691123621340266586751629857
44645309833621088720000513632839305234305983970941
The coordinates are:
Northings - use the smallest factor:
N52 [32-33].[41-43]
Eastings - use the largest factor:
W000 [13-14].[20-22]
1. There is just the slightest chance, only one chance in several billion, that there are more than two factors. If you are lucky enough to prove that there are more than two factors, then please let me know and carry on using the two largest factors you found.
You can validate your puzzle solution with certitude.