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In order for the mode to be 6, there must be more of them than any other number. In order for the mean to be 3.5, most of the distribution must lie at 3 or below to balance the large number of 6s. For the median to be 3, there must be as many scores at or above 3 as at or below 3. Thus, we choose to have most of the distribution with values 1, 2, 3 and only enough 6s to make that be the mode.
