## Friday, January 27, 2012

### An Impossible Score

There was a lot of football talk this week in my household, as the New England Patriots advanced on to the Super Bowl. I asked my husband if he can suggest any football puzzle and he recollected the following story.

A number of years ago my husband discovered that our dentist and a long-time friend happens to be friends with Tom Brady's hairdresser, and occasionally gets invited to the Patriots games. From this moment on my husband's teeth showed a suspicious attraction to the dentist's office.  One day, after breaking cement of his tooth bridge, he even found himself in the dentist's home kitchen where he bumped into... who else but the Tom Brady's hairdresser himself, who was on his way to the game. Some football talk and a few hours later they all drove by our house to pick up our son for a Patriot's game.
Next morning my husband excitedly described to me the special box seats and how he almost met Giselle, while our son proudly shared with his summer-camp friends how late he stayed up, how tasty the hot dogs of Gillette stadium were and how noisy the football crowd was.

"What was the score?"  asked his counselor.
Our son named the score he remembered.
"That's impossible!" answered the counselor.

What could possibly have been our son's answer?

Top image by Not enough megapixels, distributed under CCL.

Your thoughts and ideas accepted any time until midnight on Sunday, January 29th(EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.

Jen said...

Anything where either team scores only 1 point. The lowest individual play value is 2 (a safety), followed by 3(a field goal), then of course 6 (touchdown with no extra point). Add in the extra 1 point from a kick after a TD or two extra points for a 2-point conversion and any number greater than 1 is possible.

Tom said...

One to one. Or Anything to one. (Not much math here.)

Anonymous said...

Anything where one team had a score of "1" is impossible.

Dennis (of Dennis & Katrina)

anne-marie said...

A score of one.
I could explain why but I leave the honor to explain the different scores and explain this special score of one to a football fan. I like to watch a game sometimes but I am not a fan.

Anonymous said...

The score anything to 5?

Kim said...

Your son said 1-0.

Since you can score 2 points with a safety, and 3 with a field goal, these two alone could enable any tally to be generated other than a 1.

If it was a playoff game, it also could not have ended in any score that was a tie, but I am assuming that we're talking about a regular season game here.

Of course, impossibly high tallies (perhaps your son remembered a basketball score) could generate a "That's impossible!" response, but I assume you are looking for only scores that are mathematically possible, not just impractical or unprecedented.

[Note: also, any negative numbers would be impossible.]

SteveGoodman18 said...

The only possible scores in NFL football games are zero and positive integers.

If the son named an impossible score, he had one or both teams having either 1 point or a negative number of points.

Carrie said...

It has been a while since I have had a moment to answer one of these…
In football you can score in the following way:
2 – Safety
3 – Field Gold
6 – TD with no extra points
7 – TD with Extra point
8 – TD with 2 pts extra points

The only impossible answers are 1-0, 0-1, or 1-1.

There are lots of less likely scores, such as 6-4 or 5-2 or 156 - 4, but those above are the only impossible ones.

Carrie said...

It has been a while since I have had a moment to answer one of these…

In football you can score in the following way:
2 – Safety
3 – Field Gold
6 – TD with no extra points
7 – TD with Extra point
8 – TD with 2 pts extra points

The only impossible answers are 1-0, 0-1, or 1-1.

There are lots of less likely scores, such as 6-4 or 5-2 or 156 - 4, but those above are the only impossible ones.

Jerome said...

The most common scores are
2 for a safety (complex rules)
3 for a field goal and
6 for a touchdown.

After a touchdown there exists the possibility of 0 1 or 2 additional points.

So a tie is impossible. The rules say that a game is played until there is no possiblity of a tie.

A game ending in some score to 1 is impossible. Like 13 to 1 could not happen.

Any even score above 2 can be made by adding a safety to the previous even score.

Any odd score above 3 can be obtained the same away at least in theory.

I was trying to see if there was any way that 1 point could be scored in American pro Football and came across this rather (legal) description.

Under NFL rules, an unsuccessful extra-point is dead if kicked, but while attempting a two-point try, it is possible for a safety to be ruled if the defensive team forces the ball back into their own end zone and they recover. One point would be awarded [to the offense], instead of the two points that are normally awarded for safeties, Although the offense would still kick off, since they just scored a touchdown.[11]

This scenario would cover a situation where, for example, an offensive player fumbles the ball short of the goal line on a 2-point try, a defensive player knocks the loose ball into the end zone, and a co-defender falls on it to prevent the offensive player who fumbled from retrieving it for a two-point conversion (by rule, if any other offensive player recovers the fumble in the end zone, the ball would go back to the spot where it was initially fumbled and the two point conversion would be nullified and ruled a failed attempt). The offense would receive one point for the conversion safety, and then they would kick off as they normally would after a touchdown

If you can get your head around that, you are a better man than I dunga din.

John Wiesman said...

A score of 1 to anything.

A single point can only be scored AFTER a 6-point touchdown is made, i.e, the infamous "Point after touchdown" of PAT.

Anonymous said...

Any score that reflects a team scoring one point only ie) 1 to 2, 1 to 3 etc. My guess is the son said 1 - 0, Patriots.

Rochelle

Bean said...

1-1. Everything else is possible, as 2 ponta for a safety eliminates all even numbers, and the fact you can always add 3 for a field goal covers all the odds. So, if you rule out the practically impossible large numbers (2,000,000 to 3,000,000), the theoretically impossible score is 1-1.

Anonymous said...

0 or 100

Ilya said...

There are the following ways to score points in Football: Safety (2), Field Goal (3), Touchdown (6), Two-point conversion (2, but only with a prior touchdown), Extra point (1, but only with a prior touchdown). For our needs, it is enough to consider safeties and field goals. By using combinations of 2s and 3s, we can construct any positive integer number, except 1. Here is how: if we have an even number, we can get there using just safeties. If it is an odd number, we take one field goal, and the remaining number (if not 0) we can get by using safeties. That leaves 1, which cannot be scored on its own. So the impossible score must have included a "1" on one or both sides.

Annie said...

1 - 0 (or 1 - any #)

To review professional football scoring:
2 pts. - safety
3 pts. - field goal
6 pts. - TD
1 pt. - 1 pt. conversion (cannot be made without a TD first)
2 pts. - 2 pt. conversion ( " " " " " "

Therefore, football scoring would make a 2 possible (safety), 3 possible (field goal), 4 possible (2 safeties), 5 possible (safety and a field goal), 6 for a TD, etc. Any even number could be made with safeties alone - 2x and any odd number >1 could be made with any number of safeties plus a field goal - 2x +3. It appears that the only score that is not possible is a one. One final word: Go Pats!!!!!

Anonymous said...

Your son must have given a score of something to 1. The different scores in football:
Safety- 2 pts.
Field goal- 3 pts.
Touchdown - 6 pts.
Extra point - 1 pt.(can only be earned after a touchdown.)
From 0 points, the fewest points a team can score is 2 points. After that, any multiple of 2,3,5,7,11,13,etc. can be scored.
I think your son had the right idea, Patriots,30 - Giants 1 (ok, 2)
Go Pats!
mathmover

TracyZ said...

In pro football, points can be scored as follows:
* 6 points for a touchdown - with 1 or 2 extra points possible after a touchdown (1 for kicking the ball in the air through the goal posts; 2 for running the ball back into the end zone)
* 3 points for a field goal (ball is kicked in the air through the goal posts)
* 2 points for a safety (offensive ball carrier is tackled behind his own goal line)

With the latter two ways to score, every score that is a combination of a multiple of 2 plus a multiple of 3 is technically possible, even though some are quite uncommon. 2(x) + 3(y) = score (where x and y are any integer of 0 or above).

The only score that is not possible for a team in a pro football game is a score of 1. Therefore the only game scores that are not possible are a score in which one team ends a game with 1 point: 1-7, 1-10, 7-1, 10-1, 30-1, 25-1, etc.

Maria said...

Wow! So many football experts and Patriots fans.
You all know much more about Football than I do and you all are saying that the only impossible score is the one containing "1."

Jerome - thank you for researching the rule allowing for a unique assignment of score 1 in a specific situation. I forwarded this to some football experts I know, perhaps they can provide some layman explanation.

Meanwhile - a puzzle point for everyone participating and may your Super Bowl dreams come true.

Kim said...

Go Pats!!

Jerome said...

I thought that tie games where not allowed in the NFL.

I found out that yes they are on the regular season games, but there have not been very many.

Playoff games CANNOT end in a tie. The go for extra quarters until someone scores. When that team scores, the game is over.

Ilya said...

Score 1 is still not possible even under that special circumstance, because it implies a 2-point conversion attempt after the touchdown, so the offense would not be adding that 1 to a 0, they would be adding that 1 to at least a 6. So while obscure, it's identical in the score outcome to the normal 1 point conversion achieved by kicking the extra point.

Anonymous said...

A team can score 1, but the opposing team would have to score at least 6 points. See the logic here: http://www.thusspiked.com/2011/11/wonderful-world-of-one-point-safeties.html .

Anonymous said...

One point can be earned through forfeiture or conversion safety. So the only impossible scores are one to one-though-five.