Congrats to BoxerBailey on FTF and darkrumlover on FTS!
The geocache is not at the posted coordinates. You must solve the puzzle below to find the coordinates.
Count Factorstein & Sir Prime-a-lot have been working in the puzzle lab again! They're so excited about the Fall Favourites cache placement activity that they have cooked up a new MEGA LOGIC puzzle. What is a mega logic, you may ask? It's a kind of puzzle that I first saw in New Brunswick by cachers Ma & Pa. It's a bigger version of their micrologic series.
You can get the coordinates by solving the following: The 26 letters A - Z represent the numbers 1 to 26. Each word in the list below has a number below it. That number is found by multiplying together the number values of the letters. For example, if T = 17, H = 2 and E = 10, then THE would have value 17*2*10 = 340.
The sentences below are all pangrams, which is a sentence containing all letters of the alphabet.
To make the puzzle easier to work on, Count Factorstein and Sir Prime-a-lot calculated the prime factorizations of all the numbers. The prime factorization of a number is the unique set of primes which, when multiplied together, give the number. For example, the prime factorization of THE = 3520 is 2*2*2*2*2*2*5*11. The prime factorizations are in the table below.
So what, you ask? The prime factorization is key to solving the puzzle. But it can still be tricky, because you can arrange the numbers in various ways. For instance in the prime factor table "MY" has factorization 2*2*3*11. The two numbers representing M and Y could be 12 (=2*2*3) and 11, or they could be 6 and 22 (but not 3 and 44, since numbers must be between 1 and 26). And you don't know from that one equation which is M and which is Y. But it is possible to work out (I verified it by hand). The patterns of letters and numbers appearing in different words makes it possible to sort things out. Starting with large primes 17, 19 and 23 is a good idea. You know the largest possible number is 26, so if there's a 23 in a word, one of the letters must be a 23 (2*23 is too big, for example).
To confirm your solution and get the cache coordinates, use the checker below. Enter the 26 letters from smallest to largest, in triples seprated by ".". For example if A = 2, B = 1, C = 3, D = 4, E = 5, F = 6, ... Z = 26 you would enter BAC.DEF.GHI.JKL.MNO.PQR.STU.VWX.YZ
You can validate your puzzle solution with
certitude.
This cache owner
supports the
Association of Nova Scotia Geocaching