"Calvin":
>>>> 5 In a 12 team sports league, how many games must be scheduled
>>>> for each team to play each other team both at home and away?
>>>
>>> 132
Mark Brader:
>> 22 for each team, 132 in total, as I said. The question was ambiguous
>> three ways (two of which give the same answer).
I take it back. It's ambiguous *four* ways, at least two of which
give the same answer.
"Calvin":
> 22 games does not allow for each team to play each other team.
22 for *each team*, as I said. 11 against each other team at home
and 11 against each other team away.
> The question is not ambiguous if properly read.
In other words, it *is* ambiguous, but you imagine that only the
reading you originally had in mind is the "proper" one. Come on!
In discussion of sports leagues, it is common to speak of the total
number of games each team must play. For example, major-league
baseball has a 162-game schedule; the NHL has an 84-game schedule;
the CFL has an 18-game schedule. "How many games" can easily be
read with that meaning rather than "how many individual games"
as you intended. That's a two-way ambiguity.
Another source of ambiguity is that the words "how many games
must be scheduled for each team" may be read as grouped together.
This third reading again gives the answer 22.
Finally, in some leagues (such as the Canadian Inquisition), every
day that's a game day, all teams play. We play a 10-game schedule
in the regular season and that means that there are 10 *game days*,
although it's also true that each team plays 10 games.
I suspect that this fourth reading also gives the answer 22, but
I don't have a ready way to prove it, and it doesn't matter.
--
Mark Brader diagnostic: n. Someone who's not sure
Toronto about science and evolution, either.
m...@vex.net --Steve Summit