Simplified version of the clues:
5 of the following 8 clues are true, the other 3 are false:
1. Green and red are adjacent.
2. Blue and yellow are on the ends.
3. Clues 1, 6, and 7 are all false.
4. Yellow is directly to the right of green.
5. Clues 1 and 3 are either both true, or both false.
6. White is directly between red and green.
7. Red and green are on the ends.
8. Clue 3 is false.
If clue 3 were true, then clues 1, 6, 7 and 8 would all be false, which is impossible, because only 3 clues are false. Clue 3 must therefore be false, so AT LEAST one of clues 1, 6, and 7 must be true. Notice that clues 1, 6, and 7 all contradict each other, so ONLY one of them can be true, and the other two must be false. We know that clue 3 is false and that two of clues 1, 6, and 7 are false, which gives us 3 false clues, meaning that clues 2, 4, 5, and 8 must all be true. Based on clue 5, clue 1 must be false, since clue 3 is, and clue 7 is false, because it contradicts clue 2. This leaves clue 6 as being true.
In summary, the 3 false clues are 1, 3, and 7, and the 5 true clues are 2, 4, 5, 6, and 8. Now let's look at what this tells us about the stone placement:
From clue 2, yellow must be either on the far right or the far left, but it can't be on the far left because of clue 4. These two clues give us blue on the far left, yellow on the far right, and green directly left of yellow. By clue 6, we know that white must be directly left of green, and red directly left of white. This leaves black in the one remaining slot between blue and red.
In summary, the order is (from left to right): blue, black, red, white, green, yellow.
