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Yesterday, I read an article on the new rules imposed by the NFL for the upcoming season, and I realized how much I missed the sport. Sure, it’s been only two months since Super Bowl XLII, but it was an exciting game that rekindled my interest in pro football. So I decided to come up with my own “pretend 2009 playoffs” and create a Weekend Genius Challenge that would test your logic ability. Here it is:
It’s January 2009, and the NFL playoffs are down to the conference finals to see which two teams make it to Super Bowl XLIII. In the AFC finals, The Dolphins face the Texans. In the NFC championship, it’s the Falcons against Lions. (This is pretend, remember?) Given the following five bits of information, your goal is to determine the winner and the final score of these two league championship games:
1. The four teams combined to score 11 touchdowns, each with 1-point PATs.
2. The four teams combined to kick 4 field goals, but two teams did not kick any field goals.
3. The combined score of the two AFC teams was 1 point higher than that of the two NFC teams.
4. The Lions scored twice as many points as the Texans.
5. The Falcons scored more points than all but one of the other three teams.
And there you go. With that information, you should be able to figure out which teams won the two conference championships, along with the scores of those games. Once you think you’ve got it, type your answer into a single comment to this post. (One entry per person, please. And remember, posts are held in moderation until we approve them.)
If you’re the first to respond correctly, you’ll win a T-shirt of your choice from the mental_floss store. Good luck!
Comments (22)
Comment
Lions 14 Falcons 30
Dolphins 38 Texans 7
posted by Tom on 4-5-2008 at 9:34 am
Dolphins 35
Titans 10
Falcons 24
Lions 20
posted by Chris on 4-5-2008 at 10:11 am
Lions 14 Falcons 28
Texans 7 Dolphins 34
posted by Denise on 4-5-2008 at 10:43 am
Lions 14 Falcons 28
Texans 7 Dolphins 34
Women’s Beethoven T Shirt XL
posted by Denise on 4-5-2008 at 10:44 am
Dolphins 38 Texans 7
Falcons 30 Lions 14
posted by Robert on 4-5-2008 at 11:11 am
Phins 38 Texans 7
Falcons 30 Lions 14
posted by Robert on 4-5-2008 at 11:13 am
The Dolphins won the AFC championship, beating the Texans 38 to 7, while the Falcons won the NFC championship, beating the Lions 30 to 14.
Idioms T, Large.
posted by Jack da Bomb on 4-5-2008 at 11:21 am
Lions 14 Falcons 30
Texans 7 Dolphins 38
posted by Josh on 4-5-2008 at 11:24 am
I’m pretty sure it’s Dolphins 38, Texans 7, and Falcons 30, Lions 14. Why didn’t I wake up earlier? Rhesus L, if you’re feeling charitable.
posted by Mike on 4-5-2008 at 11:32 am
Dolphins 38 Texans 7
Falcons 30 Lions 14
posted by Mortal Light on 4-5-2008 at 11:57 am
It’s been solved but
Dolphins beat Texans 38 to 7
Falcons beat Lions 30 to 14
posted by nolalady on 4-5-2008 at 12:10 pm
D = Dolphin
T = Texans
F = Falcons
L = Lions
Say A = D + T
and B = F + L
Since combined they scored 11 touchdowns with 1 PAT each and 4 fields goals worth 3 points each:
Equation 1: A + B = 7 * 11 + 4 * 3 = 89
Also, since combined score of AFC is greater than that of NFC by 1:
Equation 2: A = B + 1
Solving the two equations in A and B:
A = 45
B = 44
So the combined score of AFC is 45 (6 touchdowns and 1 field goal?) and that of NFC is 44 (5 touchdowns and 3 field goals).
Now the winners:
Clearly from the fact that Lions scored twice as many points as Texans:
L = 2(T) and L > T
And from teh fact that combined score of AFC is greater than that of NFC by 1:
D + T = F + L + 1
Combining the two equations:
D = F + T + 1
So D > F and D > T.
Then from the fact that Falcons scored points less than only one of the other three, that team must be Dolphins since from above we know D > F.
So we get:
D > F > L > T
So in AFC, Dolphins won over Texas and in NFC, Falcons won over Lions.
If one more equation was available, one could have found out the individual team scores. Maybe I have missed something :( I don’t even watch football…and had to look up points for touchdowns, field goals and PATs!
posted by septer on 4-5-2008 at 1:04 pm
Septer, there are two facts that you are overlooking:
1. Points can only be scored in discrete 7 or 3 point intervals
2. Only 2 teams scored field goals.
These are really hard to describe in mathmatical equations. I.E. why its more of a logic problem than a math problem.
If T = 7 (1 touchdown)
Then L = 14 (7+7, two touchdowns)
A = D + T = 45, so D = 38 (7+7+7+7+7+3, 5 touchdowns 1 fieldgoal)
B = F + L = 44, so F = 30 (7+7+7+3+3+3, 3 touchdowns 3 fieldgoals)
This gives a total of 11 touchdowns and 4 field goals, with only 2 teams scoring field goals. Falcons outscore everybody but dolphins.
posted by William on 4-5-2008 at 1:26 pm
Thanks William! I knew I wasn’t using the ‘only 2 teams scored field goals’ fact. And I totally ignored the L = 2T when trying to figure out individual scores…like you said it wasn’t just solving mathematical equations!
I feel better now that I know what I missed.
posted by septer on 4-5-2008 at 2:25 pm
Falcons 31 - Lions 14
Dolphins 37 - Texans 7
posted by Brandon Arnold on 4-5-2008 at 3:30 pm
Miami 38, Texas 7
Atlanta 30, Detroit 14
posted by Jonathan Dalton on 4-5-2008 at 6:24 pm
Though I think I’m too late…
Dolphins 38
Texans 7
Falcons 30
Lions 14
- Jess
posted by Jess on 4-5-2008 at 8:23 pm
Since the right answer has been posted, I want to defend my beloved Texans!
We’re going all the way this year!
Woot!
posted by Mary on 4-5-2008 at 11:12 pm
Because of the multiplicative property of 0, there are technically two answers. Either the scores are:
HOU 7 v MIA 38
DET 14 v ATL 30
or
HOU 0 v MIA 45
DET 0 v ATL 44
0 x 2 = 0. That’s easy to forget, but it’s still true.
-Nathan
posted by Nathan Miller on 4-6-2008 at 12:53 am
Nathan, That was real nice and nerdy. :-)
posted by septer on 4-6-2008 at 11:46 am
Technically, there are other possible answers as well - through safeties.
For example, if Atlanta and Miami each recorded one, then the scores (in the intended scenario) would be DET 14 - ATL 32; MIA 41 - HOU 7.
posted by Mortimer on 4-7-2008 at 10:02 pm
William,
T does not equal 7. Instead T=6, PAT=1 (Point After Touchdown) and TPC=2 (Two Point Conversion). So any T can have a PAT or TPC or none of the above added to it.
posted by Brad on 4-8-2008 at 8:21 pm