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Quarry Conundrum puzzle; math related?
Last night I was helping my girlfriend solve the dwarven puzzle in Graystone Quarry in Orsinium. I've heard from several people that, without spoilers, the solution to the puzzle is only to be obtained via trial and error. But when I noticed that each focus had a total of eight possible positions on each ring, I began to wonder... can this be solved with reference to base 8 math? Here's my logic on this:
Each focus begins at a neutral position of zero. The inner ring's position needs to be 1, the middle ring 7, and the outer ring 4. Let's call these rings x, y, and z respectively. The number of times each ring rotates is irrelevant as long as the focus aligns with the light.
This means that the inner ring needs to move either 1, 9, 17, 25... etc times.
The middle ring needs to move either 7, 15, 23, 31... etc times.
The outer ring needs to move either 4, 12, 20, 28... times.
Since there are eight possible references to the focus' location, base 8 math can be used to determine the ideal number of times each focus has moved, but what's more important is the final digit. Base eight counts from 1 to 7, and then to 10, which is technically the number 8 in disguise.
Every time a lever is flipped, 1 gets added to two of the values corresponding to each ring.
The middle lever adds a value of +1 to x and z.
The right lever adds a value of +1 to y and z.
The left lever adds a value of +1 to x and y.
So as long as the digit in the ones place matches the ideal value of each variable, the puzzle is solved.
That's as far as I got. Is there actually some means of creating a mathematical model that will lead to the solution?
Each focus begins at a neutral position of zero. The inner ring's position needs to be 1, the middle ring 7, and the outer ring 4. Let's call these rings x, y, and z respectively. The number of times each ring rotates is irrelevant as long as the focus aligns with the light.
This means that the inner ring needs to move either 1, 9, 17, 25... etc times.
The middle ring needs to move either 7, 15, 23, 31... etc times.
The outer ring needs to move either 4, 12, 20, 28... times.
Since there are eight possible references to the focus' location, base 8 math can be used to determine the ideal number of times each focus has moved, but what's more important is the final digit. Base eight counts from 1 to 7, and then to 10, which is technically the number 8 in disguise.
Every time a lever is flipped, 1 gets added to two of the values corresponding to each ring.
The middle lever adds a value of +1 to x and z.
The right lever adds a value of +1 to y and z.
The left lever adds a value of +1 to x and y.
So as long as the digit in the ones place matches the ideal value of each variable, the puzzle is solved.
That's as far as I got. Is there actually some means of creating a mathematical model that will lead to the solution?
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ghastley✭✭✭✭✭
✭Yes, but you'll do better by assigning variables to the number of operations of the levers. I'll use c, l, r to better remember which is which. It's just a simple simultaneous equations problem.
center lever moves inner and outer rings, left moves inner and middle, right moves outer and middle, so
c + l = total moves of inner ring - must use 9 here as we can't add two non-zero numbers and get 1
l + r = total moves of middle ring = 7
r + c = total moves of outer ring = 4
Note that since each lever adds two moves, the overall total moves must be even, or the puzzle would be impossible.
Add them all up and you find that 2c + 2l +2r = 20, subtract 2l + 2r (i.e. double the middle ring moves) and the result is 2c, so divide by two to get the moves of the center lever. (20 - 14) / 2 = 3.
Similarly, left is (20 - 8) / 2 = 6 and right is (20 - 18) / 2 = 1
All assuming your numbers are right. Base 8 arithmetic doesn't really figure in, except that we had to make that total a 9 instead of a 1.It doesn't matter in which order you move the levers, as long as the counts are right, and you've reset the puzzle first.
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