Schooley Balance Scale II Mystery Cache
Schooley Balance Scale II
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Difficulty:
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Terrain:
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Size: 
(micro)
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Cache is a traditional hide approximately 10 ft into the woods. Difficulty is mainly in solving puzzle. Cache container is 4 inch pill bottle.
On December 30, 2008 the Schooley Balance Scale cache was moved, algorithm for finding coordinates was changed, old cache was archived, and this new cache was created. On May 3, 2019 moved cache as the path to the cache had disappeared over the years. To find the location of this cache, you need to solve a problem associated with a balance scale and 12 balls. A balance scale doesn’t measure a weight but indicates whether the objects on one side of the scale are heavier or lighter that the objects on the other side of the scale. The 12 balls are all a different color to distinguish them from one another. The 12 balls either (1) all weigh the same or (2) one of the balls is either heavier or lighter than the other 11. Let N be the minimum number of measurements with the scale required to guarantee one can determine whether (1) all the balls are identical and (2) identify the ball that is different and to determine whether the ball is heavier or lighter than the other 11. Let M be the total number of balls NOT put on the scale on the first measurement. Note: M is unique when minimizing the number of measurements. When measuring the (12-M) balls, if the scale is not balanced, the number of these (12-M) balls that can be used for the second measurement is not unique. Let K be the minimum number of the original (12-M) balls you put on the scale for the second measurement and let L be the maximum number of the original (12-M) balls you put on the scale for the second measurement. When measuring the (12-M) balls, if the scale is balanced, let P be the number of balls not used in the first measurement that are used in the second measurement. The coordinates of the cache are N 39 10.ANP and W 076 57.MBL where A = N - P B = K - N The key to solving puzzle is to note that one obtains information about balls both on and off the scale on each measurement. If scale tips, one knows that certain balls are either heavy or light and that balls not on the scale are not the odd ball. If the scale balances, all balls on the scale are eliminated, and only balls not on the scale are possibly the odd ball. A check sum for A, B, L, M, N, P is 18
Additional Hints
(Decrypt)
Arkg gb n ybt jvgu n ebpx pbirevat epnpur