Source: Gabe, citing Hard to solve brain teasers. Original.
1 7 6 4 8 3 5 2This is made simpler by a couple of realizations:
oeo or ooe e e e e oeo ooeOnly the second can satisfy both of the previous requirements.
So now we have o72 or o76 4 8 4 8 oo6 oo2There is enough information to find the remaining numbers and only the second pattern works. So not only do we have an answer but we know it is the unique (but for rotations and reflections) solution.
Probabilities for various rolls:
Sum (with +) Prob. Difference (with -) Prob. 2 1/72 0 6/72 3 2/72 1 10/72 4 3/72 2 8/72 5 4/72 3 6/72 6 5/72 4 4/72 7 6/72 5 2/72 8 5/72 9 4/72 10 3/72 11 2/72 12 1/72Overall probabilities for each roll:
Roll Prob. 0 6/72 1 10/72 2 9/72 3 8/72 4 7/72 5 6/72 6 5/72 7 6/72 8 5/72 9 4/72 10 3/72 11 2/72 12 1/72Average roll is easily computed from the above.