Reader Joachim noticed a flaw in the fun diversion test posted before, so I decided to rectify the situation. This entailed making a new test with manually assigned maps to ensure every layout matches perfectly, which they do. Several hours later, for those who remain interested, here is the result.
Each cube pair is the same cube. Each single cube matches one of the cube pairs. Can you figure out which single cubes belong to which pairs? Many will look the same at first glance, but they are not the same between numbered columns or ranks. Match cubes identified with a letter to the numbered column that contains the matching cubes. For extra credit, One cube set was duplicated, but different faces are visible. Meaning, there are 2 right answers for this cube set and its duplicate.
NOTE: Assymetrical pip arrangements may appear in both possible orientations. Or to put it another way, they do.
ALSO: This puzzle is much more difficult than the last one. To solve, you must solve the entire page.
Some additional clues:
Note: Pattern numbers are unrelated to image numbers in test.
ANSWERS BELOW
It seems that we (the Substack author and I) are now (probably long since) the only two watching this thread, so I won't be denying anyone a chance to attempt to solve by listing/explaining my answers, which show how elimination did not quite work to solve for all 18 pairs, for me at least.
First, here are the possibilities for each pair considered in isolation:
1. E, G, J, R
2. N, O
3. N, P
4. I, N, Q
5. I, Q, R
6. M, N
7. K
8. D, E, F, G
9. D, E, F, G (identical cube to 8)
10. I, N, Q (not necessarily identical to 4, but could be--we don't know the orientation of the "2" pattern in pair #4)
11. L, M, O
12. F
13. B
14. A, D
15. A, M, O
16. H
17. C, D
18. I, Q, R (not necessarily identical to 5, but could be--we don't know the positions of the "3" and "6" faces or the orientations of the "3" and "6" patterns in pair #18)
Here, for reference, is a list of the ambiguities in the 18 pairs:
1. has three possible configurations because we see two sets of three sides but not the relation between the two sets.
2. has two possible configurations because we don't see the orientation of the "6" pattern
3. has four possible configurations because we don't see the positions of the "2" and "5" faces and the orientation of the "2" pattern
4. has two possible configurations because we don't see the orientation of the "2" pattern
5. has no ambiguity
6. has two possible configurations because we don't see the positions of the "1" and "4" faces
7. has two possible configurations because we don't see the orientation of the "2" pattern
8. has no ambiguity
9. has no ambiguity
10. has no ambiguity
11. has four possible configurations because we don't see the positions of the "2" and "5" faces and the orientation of the "2" pattern
12. has two possible configurations because we don't see the orientation of the "6" pattern
13. has no ambiguity
14. has no ambiguity
15. has two possible configurations because we don't see the orientation of the "2" pattern
16. has no ambiguity
17. has no ambiguity
18. has eight possible configurations because we don't see the positions of the "3" and "6" faces and the orientations of the "3" and "6" patterns
Looking from "solution" images to pairs, several eliminations can be found.
Choice "C" is only listed (above) as possible answer for pair 17, so we assign those together. Similarly, choice "J" is only listed as possible for pair 1, so we associate those. Again, choice "P" is only listed as possible for pair 3, so we associate those. With pair 1 eliminated from consideration, E and G (identical solution images) taken together, are only listed as possible for pairs 8 and 9, so we associate those. With pairs 8, 9, and 17 eliminated from consideration, D is only listed as possible for 14, so we associate them. With 14 eliminated from consideration, A is only listed as possible for 15, so we associate them. With 15 eliminated from consideration, L is only listed as possible for 11, so we associate them. With 11 eliminated from consideration, M is only listed as possible for 6, so we associate them, and O is only listed as possible for 2, so we associate them.
So we are left with pairs 4, 5, 10, and 18 and solutions I, N, Q, and R.
(Since choices I and Q are identical (with rotation), there there will at least be a two-fold ambiguity that is unavoidable.)
Pairs 4 and 10 are identical as far as we can tell, and pairs 15 and 18 are identical as far as we can tell, but the problem description says there is one (and we can assume only one) pair that is duplicated, and since pairs 8 and 9 are unambiguously the same, the cubes represented in image pairs 4 and 10 must be different from each other, as well as the cubes represented in image pairs 5 and 18.
For the pairs 4 and 10, this means that the cube in pair 4 must be the same as the cube in pair 10 but with the "2" pattern rotated 90 degrees. This eliminates choices I and Q as possibilities for pair 4, so we assign the remaining choice, choice N, to 4. But pair 10 still has I and Q as (identical) possible matches.
For the pairs 5 and 18, pair 5 has no ambiguity, but pair 18 has 8-fold ambiguity, so requiring that pair 18 must be different from pair 5, by itself, only eliminates 1 of 8 possible configurations for pair 18. We can narrow this down by looking at the three solution options for pair 18: I, Q, and R. Each of I, Q, and R shows a "6" side location -- and a "6" pattern orientation -- consistent with pair 5. So if pair 18 is to find a match among I, Q, and R *and* be different from pair 5, it can only be different from pair 5 in the orientation of the "3" pattern. But none of I, Q , and R show the "3" pattern orientation, so this does not help in making a choice among them distinguishing pairs 5 and 18.
So now we know the exact configurations of the cubes represented by the remaining pairs -- pairs 5, 10, and 18 (18 being the same as 5 but with the "3" pattern rotated 90 degrees). But for pair 10, I and Q are [identical] matches, and for pairs 5 and 18, I, Q, and R are all matches. So there is still a four-fold (or eight-fold, counting pairs 8 and 9) ambiguity in the problem solution as a whole.
Final list:
1. J
2. O
3. P
4. N
5. I, Q, R
6. M
7. K
8. E, G
9. E, G (identical cube to 8)
10. I, Q
11. L
12. F
13. B
14. D
15. A
16. H
17. C
18. I, Q, R
There might be a flaw or two in this set also, if I am reading (and rotating) correctly.
First, choices E and G are the same image.
Second, the two views of cube #1 show all six faces of the cube. That means we cannot determine the orientation of the faces in the top image relative to the faces in the bottom image, or, put another way, the "1" face of the top image could be directly opposite the "2", the "5", or the "6" face of the bottom image. So there are three possible configurations for cube #1.
Maybe this was intended, but it apparently contributes to more than two possible answers for cube #1. Choice E (and choice G since it is the same) are rotations of the bottom image of cube #1, so they match the information given for cube #1. Choice J is a rotation of the top image of cube #1, so it also matches the information given for cube #1. Choice R also seems to be consistent with both images given for cube #1. So, E, G, J, and R all seem to fit.
For cube #2, choices N and O (and no others) seem to be consistent with the images shown. This of itself is no problem--maybe this is one of the two identical cubes--I have not gone through them all.
Third, for cube #3, only 4 of the six faces are visible in the two images--both the "2" face and the "5" face are not shown. This means there are two possible configurations for cube #3 (really four, taking into account the two possible orientations of the dots on the "2" face). Maybe this was intended, but it appears to result in 2 possible answers for cube #3--both choice N and choice P appear to be consistent with the images given. But this can't be the other identical two-answer cube (if I understand the description correctly) because the two answers are not the same two answers as for cube #2.
(This set is harder than the original, and would be even without the possible flaws. The above represents about 60-90 minutes of checking and rechecking. And it was only on the first three cubes!)