How many 6−sided dice with values on each side in the set {1,2,3,4,5,6} are there with the property that when rolled twice, for each integer 2≤k≤12, there is positive probability that the sum is exactly k? Note that not every value in the set necessarily needs to be used and that two dice are considered indistinguishable if they contains the exactly same amount of faces corresponding to each value in the set, regardless of the labelling of the sides. Assume each side appears with equal probability.
