I met someone who looks a lot like you
She does the things you do
But she is an IBM
She is the latest in technology
Almost mythology
But she has a heart of stone
She has an IQ of one-thousand-and-one
She has a jumpsuit on
And she's also a telephone
- Electric Light Orchestra -
The cache is not at the posted coordinates
To locate the cache, you will need to solve a puzzle, the only reasonable method for which is by writing and executing a computer program.
At the bottom of this listing you will find 60 numbers, divided into 10 groups of 6. The west coordinate of the cache can be determined by computing the sum of one number from each of the 10 groups. The north coordinate can be determined by computing the sum of one number from each of the first 4 groups.
The trick is determining which number in each group of 6 is the correct one. In case you consider attempting the solution manually, be aware that there are 60,466,176 possible solutions (6*6*6*6*6*6*6*6*6*6) for the west coordinate and 1,296 (6*6*6*6) for the north coordinate. Please correct me if I'm wrong in this assumption.
The exact north and west coordinates occur only once in the possible solutions. However, there are many very near hits. To narrow down to the exact numbers, you will need to include the following criteria in your programming:
Consider both coordinates as single numbers. For example, the numbers associated with the posted coordinates would be 4,045,134 and 11,148,430.
The cache is less than .040 minutes, both latitude and longitude, from the posted coordinates.
The north coordinate occurs only once within the distance range specified above. West coordinates within the above range occur many times.
The number representing the west coordinate is odd.
The sum of the individual digits of the west coordinate is 28.
The west coordinate ends in a 1, 2, 4 or 8.
Please don't hesitate to pose questions, suggestions or comments! If you enjoyed this puzzle, please recommend it to others who may be interested. No, it's probably not going to be a big seller!
Notes on the development of the puzzle:
I've wanted to post a programming-required puzzle cache for quite some time. When I came up with this idea, I assumed it would be very easy to create. Wrong! I have spent far more time developing it than will likely be required for the solution. My goal was to include a large enough list of numbers that a manual solution would be virtually impossible and that a programming solution would require a fair amount of number crunching.
My first approach was to generate the numbers manually (just by making them up) and then run a program to count the number of hits and near hits. I assumed that the exact numbers would occur only once and that there would be no near hits. That assumption was way off, as my first attempt yielded hundreds of near hits (within the .040 distance range) and 8 exact hits. I found that amazing, considering the size of the numbers involved. However, when you consider the 60 million + permutations, I guess that explains the frequency.
I then spent quite some time randomly changing numbers in the list with the hope of narrowing down the hit list, but was not successful. Finally, I realized that by inflating many of the numbers in the list which were not part of the solution, I could force the vast majority of summations to be larger than the coordinates (which is why the smaller north coordinate occurs only once). However, the correct numbers in each group of 6 then stood out pretty obviously from the others, since they were smaller.
Finally, I resorted to writing a program which would randomly generate all of the non-essential numbers in each list, and then loop over and over, with a different set of random numbers each time, counting the number of hits. This led to accepting solutions where the exact numbers occurred only once, but many near hits were possible. With the additional narrowing-down parameters, I was able to finally get an acceptable list, although the generating program ran for many hours before meeting the criteria.
An interesting observation: My original program had an on-screen counter which displayed the number of executions of the loop each time through (from 1 to 60,466,176). It took well over an hour to run. With the screen display removed, however, the same program runs in about 3 or 4 minutes.
I used Visual Basic V6. Please post your language of choice in your log.
Hopefully, your solution will be easier!
If you have enjoyed this puzzle, here are some more Programming Caches.
Here are the data (hopefully copy-and-pasteable into your program):
598125
1195047
1048117
2142802
646879
839092
1950374
1368592
1218692
2071321
2078088
517849
2018514
1775987
972140
1897428
1934499
1044518
952851
1764608
2112035
1017429
1287735
900413
1427394
1798343
1190761
1318674
1389896
811757
1518060
1112337
1944434
1546657
2144387
1167689
1109247
1517359
1643104
1142560
1420322
1086241
1537946
2157887
2027591
1865835
2176224
1208445
2093132
552868
1378216
1324555
1555687
2011169
1885726
1449987
1635596
1317029
587633
1879723
EOF!