Two Ends Mystery Cache
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Difficulty:
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Terrain:
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Size: 
(micro)
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in our disclaimer.
There is absolutely nothing wrong with the coordinates above. I'm sure they would take you to a very nice location where you could enjoy God's creation. However, if you want to find this cache, I don't recommend going there; I recommend solving the puzzle instead.
In Counting Tiles, I introduced you to a friend of mine who I called "Alan." I had many wonder about Alan. Some thought that I made him up, because no one could be that strange, right? Others thought I made him up because obviously I have no friends. And others just wanted to hear more about this weird dude, so I decided to use this cache to tell you a story from Alan's childhood. First however, I want to state again: any similarity to any local cacher of the same name is entirely coincidental and unintended. No ... really. C'mon, would I tell stories about a guy like that and use his real name?
So, when Alan was a child, he was very taken with numbers. He loved a game called "Two Ends." In this game, an even set of integers is laid out in a row. Two players take turns selecting a number from the row, but they can only select a number from one of the ends of the row. After all numbers are selected, the player with the highest total wins.
One day Alan was playing with one of his little friends; for anonymity let's call her "Kristi." (Please see caveat above about any similarity of this name to a local cacher.) Alan laid out 4 numbers in a row:
9 5 12 8
Alan said "I'll go first," and selected the 9. Kristi selected the 8, then Alan selected the 12 and Kristi took the 5 which was the last remaining number. They added them up and Alan celebrated because his total of 21 was more than Kristi's total of 13. They decided to play again, and this time it was Kristi's turn to go first. They laid out four more numbers:
10 12 7 8
Kristi picked 8, and Alan immediately laughed at her. "You didn't pick the biggest one!" Kristi just smiled and said "let's play it out." Well, they did ... and Kristi won 20-17. Alan realized that the best strategy for this game didn't always involve picking the biggest number available. When he grew up to be a "big boy" he realized that the precise way to word the principle was "the greedy strategy does not always arrive at the optimal solution." They started another game with the numbers:
5 9 3 21 15 11
It was Alan's turn to go first, but before Alan could pick a number, Kristi announced to him "if you had a brain in your head, you should win this game by 18 points." Well, little Alan didn't play his best and didn't win by 18, but he did win. In the following game, Kristi again announced the minimal amount of points she would win by. In fact, from that time on, Kristi could always tell Alan at the beginning of a game how many points the player going first should win by. Alan didn't always achieve that when he went first, or hold Kristi to that minimum when she went first ... but she was never wrong. As you can imagine, this didn't sit well with Alan ... and soon he would no longer play this game with Kristi.
Poor little Alan. Perhaps the frustration of this is what caused him to start counting tiles. Perhaps you can make him feel better by coming up with a technique to determine how many points the 1st player will win by, assuming both players make the optimal choice each turn. Or maybe Kristi is just a genius, and no one else will be able to replicate her skill at this game.
For this puzzle, assume the coords are of the form: N39 AB.CDE W84 VW.XYZ. To get the 10 missing digits, you will need to solve 10 scenarios of the Two Ends game. For each scenario, determine the number of points that the 1st player will win by, assuming that both players make an optimal choice every time they pick a number. If the optimal minimum score for the 1st player is greater than 9, use the rightmost digit of the score as your digit for the puzzle. So, if the 1st player's optimal score is 25, use 5 for the digit.
Just to make you work a little bit, some of the scenarios may involve quite a few numbers. I will give you the number of numbers for each scenario in parenthesis. P.s., someone might want to help Alan ... he's pretty frustrated right now. (Of course, that's assuming you know his real name.)
Digit A (2 numbers)
4 8
Digit B (4 numbers)
10 12 7 8
Digit C (60 numbers)
949 228 159 127 244 92 526 168 322 913 199 468 243 980 391 200 593 857 76 496 749 578 597 863 612 125 638 736 589 504 243 538 83 401 16 326 845 893 493 166 805 43 633 47 23 24 599 615 232 674 462 332 603 58 546 567 183 535 654 123
Digit D (24 numbers)
100 304 166 849 478 770 991 42 114 85 425 799 91 333 958 401 988 684 709 513 737 672 156 994
Digit E (6 numbers)
9 21 15 23 3 8
Digit V (4 numbers)
4 4 4 4
Digit W (6 numbers)
8 3 5 7 1 9
Digit X (14 numbers)
146 186 85 439 843 122 79 49 152 740 616 451 678 200
Digit Y (36 numbers)
874 628 331 763 293 187 900 838 797 245 674 86 550 959 26 65 65 804 968 497 265 588 353 336 992 331 634 543 382 847 627 606 475 309 368 119
Digit Z (12 numbers)
851 820 320 523 172 513 943 605 974 152 8 542
You can validate your puzzle solution with certitude.
Additional Hints
(Decrypt)
Chmmyr: Nyna fnlf "nyjnlf cvpx gur evtugzbfg ahzore." Ohg erzrzore, Xevfgv nyjnlf orng uvz.
Uvqr: Thneq envy