What is the total number of distinct sums possible from tossing six, six-sided dice? I was reading The Ascent of Money by Niall Ferguson, and he writes
"... he [John Law] wagered 10,000 to 1 that a friend could not throw a designated number with six dice at one throw. (He probably lost that one [gamble] too, since here are only 31 possible outcomes: the chance of throwing 21 is about one in ten." (the italics are mine)
How does one figure out that there are only 31 distinct outcomes (i.e. sums)? 
Not sure what tags would be fruitful. So if you guys have suggestions for tags, rather than answers please inform me.

Well the minimum is all $1$s and the maximum is all $6$s so you have $6\times 6 - 6\times 1 + 1 = 36 - 6 + 1 =31$ possibilities.
