5
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The 1 x 1 x 2 die with new configuration was created from 2 dice (w/ opposite faces total 7) that were glued together on one of their faces. If this long die is rolled twice, the sum of non-repeated results can be equal to 5, 6, 7, 8, 9,11,12,13,14,15,16 or 20. What are the glued faces of the 2 dice?

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  • $\begingroup$ Perhaps i'm misunderstanding, but how can 5 be the sum of two rolls? Given that the dice is gonna land with two faces up, the rolls would have to be 2 + 3. In order to get 2, it'd have to be both 1 faces on top, then how would you be able to roll a 3 next time, which would require a 1 and 2 face on top $\endgroup$ – indubitablee Jun 22 '17 at 16:09
  • $\begingroup$ @indubitablee-the die can also land on 1x1 faces though less likely $\endgroup$ – TSLF Jun 22 '17 at 16:20
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    $\begingroup$ @TSLF haha understood, thanks! #gravityRebels #momentumShmomentum $\endgroup$ – indubitablee Jun 22 '17 at 16:22
  • $\begingroup$ What does "sum of non-repeated results" mean exactly? $\endgroup$ – Gareth McCaughan Jun 22 '17 at 16:23
  • $\begingroup$ @GarethMcCaughan Presumably that rolling the same side twice in a row wouldn't be counted. Looking at the results, this must be the case, as if duplicates were counted, the smallest roll is necessarily even. $\endgroup$ – Ian MacDonald Jun 22 '17 at 16:29
4
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The two hidden faces are

3 and 5

The net of the new die is:

+-----+ | 1 4 | +---+-----+---+ | 4 | 2 1 | 2 | +---+-----+---+ | 6 3 | +-----+ | 5 6 | +-----+

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  • $\begingroup$ note the chirality $\endgroup$ – TSLF Jun 22 '17 at 17:00
  • $\begingroup$ How did you work that out? I'm struggling to think of appropriate logic tht isn't just brute force.... $\endgroup$ – Chris Jun 23 '17 at 16:32
  • $\begingroup$ @Chris The 5 couldn't be made from two double faces, as there aren't enough 1s. I guessed that it was made of a double face and a single face. That only left two possibilities, and one happened to be right. The rest was pretty much just following the implications. $\endgroup$ – Mnemonic Jun 23 '17 at 16:46
  • $\begingroup$ @Chris-5 can be made from a double face and a single face: [22]1],[21]2] & [11]3] $\endgroup$ – TSLF Jun 24 '17 at 18:24

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