100s Game Mystery Cache
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Difficulty:
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Terrain:
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Size: 
(micro)
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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. If you want to find this cache, I don't recommend going there; I recommend solving the puzzle instead.
A game of 100’s consists of a sequence of deals. In each deal, the player will have six cards, each of which contains a single digit. The player will choose 4 of the cards, in two sets of two, to play for this deal. Each set of two cards forms a 2-digit number, and the two 2-digit numbers formed by the four chosen cards are added together. The goal for each deal in the game is to choose the two sets of two cards which add to form a sum as close as possible to 100. Your score for a particular deal (the penalty) will be determined by how close to 100 your sum is. It doesn't matter whether your sum is above or below 100; e.g., 97 and 103 both would result in a score of 3 for that deal.
For example, assume you have the cards ‘6’, ‘7’, ‘5’, ‘3’, ‘5’, and ‘6’. You might chose the sets of <6,5> and <3,5> as your four cards, which represent 65 and 35 and total 100. Thus, you would get a penalty of zero for this deal. A game consists of multiple deals. After a particular deal, the two cards not chosen (in the example above, a ‘7’ and a ‘6’ were not used) are kept for the next deal. The next deal then begins by adding four new cards, which forms a 6-card hand. The player again chooses 4 of the cards from her hand to try to minimize his/her penalty.
You are to play this game, trying to minimize the penalty from a sequence of deals. In a normal sequence of play, you will not know the cards which will come next, so you must pick the best solution for each hand without using any knowledge of what cards are coming up in the future. In other words, you should choose the best play for a given hand without worrying how that decision might impact future deals.
Your overall score for a game is the sum of the penalties for all of the hands played.
For this puzzle, you will be given 10 different games, each consisting of a series of hands. Each game will produce one digit for the cache coordinates. For each game, compute the overall penalty using the rules explained above. Then, use the least significant digit (the rightmost digit or 1s place) as your answer for this digit of the coordinates. For example, if the total penalty for a particular series of hands is 13, then the digit you have found for the coordinates is 3. Got it?
For the game specified as: 345634 9583 the first hand consists of the numbers 345634. The optimal play is 44 + 56 = 100, for a zero penalty. For the 2nd deal of this hand, the two unused cards (3, 3) are combined to the next four cards to form a hand of 339583. The best play for this deal is 39 + 58 = 97, for a penalty of 3. For the entire game (in this case consisting of two hands), the total penalty was 0 + 3 = 3. Thus, this game would produce the digit 3 for the coordinates.
Of course, we wouldn't want to have too many simple games like that, or the puzzle would be too easy. On with the puzzle .... You can assume N39 and W084.
Game 1: 345634 5858
Game 2: 772878 8328 6666 3535 3685 4708 1256
Game 3: 163807 1546 8362 2456 4657 2985 1277 8351 2499 6835 1746 8364 2756 4657 2985 3287 8351 1479 6875
Game 4: 713984 1246 4347 8869 1258 5563 4569 5521 5482 9298 7406 3619 2463 5382 3954 6997 8123 9634 5882 2066 5361 6973 6237
Game 5: 317591 8351 3156 1427 9759 8238 4369 8032 7313 3521 7642 8787 8345 4956
Game 6: 039786 9225 8450 1137 6320 4768 7637
Game 7: 514073 1248 4347 8769 1234 5576 4563 5321 5472 9268 7446 3513 2443 5372 2954 6938 8123 9634 5873 2166 5361 6183 7238
Game 8: 884422 6424 6543 2356 6839 4368 5859
Game 9: 981453 6212 8357 3371 6668 3644 9238 5732 4972 8357 4499 2139 5991 2157 7758
Game 10: 978657 3210 5185 7721 5402 1017 5585 3210 5392 7711 6135 1017 5555 3810 5092 7834 5004 1017 3674
As usual, there is the easy way and the hard way to solve this one. I recommend the easy way.
You can validate your puzzle solution with certitude.
Additional Hints
(Decrypt)
Hfr lbhe pbzchgre!