There is nothing at the posted coordinates, except for a lamp post with some numbers on. These numbers have no relevance to the puzzle in any way. I just simply chose an arbitrary lamp post on Station Road. The cache is a short walk away.
This puzzle has a nice mathematical solution that you can work out with pen and paper. It does not require writing any computer programs, a simple calculator will suffice. However, solving this with pen and paper is very challenging. It does not require any advanced maths theorems, though it should still take the average person a lot of research in order to solve.
The puzzle involves using the sums of digits in various bases. Here is an example:
Take the number 3894 (in base 10). In hexadecimal (base 16) this number is 'F36'. To add the digits up of such a number, this puzzle uses their numerical values corresponding to each digit. Since we operate in base 10, lets convert each digit into base 10 numbers. Converting each digit to base 10 we get: 15, 3, 6. The sum of these numbers is 24. Converting 24 back into hexadecimal we get '18'. As far as this puzzle is concerned, the sum of the digits of 'F36' in hexadecimal is '18'.
This puzzle also uses base 30 (Trigesimal) and base 62 (Duosexagesimal). To represent base 30 this puzzle uses the Natural Area Code system. Specifically its 30 digits (listed in order so that their values go from 0-29) are: 0-9 followed by A-Z excluding A,E,I,O,U,Y. Be careful as this is not the system a lot of websites use. To represent base 62, the 62 digits this puzzle uses (listed in order so their values go from 0-61) are: 0-9, a-z followed by A-Z. This puzzle represents octal and hexadecimal as usual.
For example, converting the number 77 (base 10) into the above base 30 system gives you '2K'. Converting 77 (base 10) into the above base 62 system gives you '1f'. Converting 111 (base 10) into the above base 62 system gives you '1N'.
Now for the puzzle itself:
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I’m thinking of a 6 digit number (in base 10).
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The sum of its digits in base 10 is 32.
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If I convert the original number to Octal, the sum of its digits is '24' (also given in octal).
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If I convert the original number to Hexadecimal, the sum of its digits is '1D' (also given in hex).
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If I convert the original number to Trigesimal (base 30), the sum of its digits is '2V' (also given in base 30).
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If I convert the original number to Duosexagesimal (base 62), the sum of its digits is '1X' (also given in base 62).
To clarify, each time, the above puzzle takes the 'original number' that I was thinking of, converts it into a specific base, adds the numerical values of the digits corresponding to these bases, converts this sum back into the specific base before finally giving you the result.
One you have the 6 digit number that I was thinking of, multiply the 1st 3 digits by the last 3 digits. Then multiply this by the number that I was originally thinking of. Next subtract 415219933 and then finally take the last 8 digits of the result. You should now have an 8 digit number ABCDEFGH. The coordinates of this cache are: N52 1A.BCD E000 0E.FGH
To check your answer I've provided a Certitude checker, however this uses a “keyword” solution. Instead of entering the coordinates, you must enter the digits corresponding to ABCDEFGH followed by (no spaces) the number I was originally thinking of.
You can validate your puzzle solution with certitude.
You do not need to give Certitude access to your geocaching account, but if you do it is via Groundspeak’s official geocaching API (Application Programming Interface). Specifically this means Groundspeak controls what external apps / websites can access via its API it provides.
The only reason Certitude asks for access to your geocaching account, is literally to put your name up on the leaderboard of puzzle solvers. Again this is purely optional. If you do not wish to add your name up on leaderboard, either make sure the “stay anonymous” box is checked, or don’t sign in at all. Please note: putting your name up on the leaderboard (via entering in the correct number into the checker while you are signed in and the box is not checked) is a permanent action. This means you (or I) cannot remove your name from the leaderboard.
In addition, if you wish to automatically update the cache page with the solved coordinates (to save you manually typing these in), you can drag the link Certitude provides you with into your browser's bookmark bar (you may need to enable it), and then click the bookmark from the cache page.
I've given 4 puzzle hints to assist pen and paper solvers. Despite these hints, it is still a tricky puzzle. Now FTF is gone, I'll happily help people out if they ask nicely. If anything about the puzzle itself (beyond how to solve it) doesn't make sense, please let me know. I want it so that people can easily understand what the puzzle is asking of them, just not how to solve it. I will then publicly clarify things if need be. If you think you solved this puzzle a different way from me, and are interested in seeing my solution for the puzzle, please also drop me a message.
The cache can be accessed from either Longstanton (the village), Willingham, or the Longstanton Park and Ride Busway stop. Alternatively if you can find a place to park on Station Road it can be accessed from there.
Be warned, there are quite a few nettles that you need to avoid to get to the cache. I strongly advise you wear trousers for this very reason.
Please note: the outer container doesn’t properly seal, however the inner container should be perfectly watertight. If this poses a problem I will resolve this one way or another.
In addition, this cache is terrain 3 for a reason (more details provided in Certitude). Specifically you can quite easily slip if you’re not careful. Please ensure this is carefully hidden from where people walk.
The difficulty 4 rating refers to the puzzle. The actual hide is around difficulty 2.
Please also report if the coordinates are slightly off so I can update them. I spent an hour faffing around trying to get accurate coordinates (as the satellite disagreed with them). I hope these coordinates are good, but my GPS was being a little unreliable (despite reporting a high accuracy) in the location.
The cache contains some mathematical themed items, as well as some toys that I used to have when I was younger (that would otherwise go to a charity shop). There should be space for a small travel bug, though it's quite full as it is.
If there's any problems with this cache, feel free to post a NM or contact me.
Please also note: I am on holiday for 12 days starting Monday the 7th. If there's internet I hope to be able respond to messages, though there may not be. I will respond to any maintenance queries when I get back.
Congrats S&AT for being first to solve @8.49am, specifically only 82 minutes after this cache was published. Also congrats S&AT for being first to find.
Good luck, and let the challenge begin...