tag:blogger.com,1999:blog-15628310.post8230694909917491252..comments2021-01-21T13:53:28.761-05:00Comments on Question of the day: Football puzzleAnonymoushttp://www.blogger.com/profile/18153935609499338685noreply@blogger.comBlogger11125tag:blogger.com,1999:blog-15628310.post-35070127487066879632009-05-14T10:00:00.000-04:002009-05-14T10:00:00.000-04:00I'm not big on football but I would have to say th...I'm not big on football but I would have to say there's several different ways to score 20 points but no one said it would be easy.Jazzy F. Babyhttps://www.blogger.com/profile/18330560315501497804noreply@blogger.comtag:blogger.com,1999:blog-15628310.post-52149834455758550622007-01-23T19:05:00.000-05:002007-01-23T19:05:00.000-05:00Sean, the formula takes care of that. The only ti...Sean, the formula takes care of that. The only time you can score 1 point by itself is if the other team forfeits.<br /><br />Mr Don, I agree it doesn't matter. I was just trying to make my answer to cover all possibilities.Anonymoushttps://www.blogger.com/profile/18153935609499338685noreply@blogger.comtag:blogger.com,1999:blog-15628310.post-70443792630380823652007-01-23T18:24:00.000-05:002007-01-23T18:24:00.000-05:00Mike, does it really matter in which order you sco...Mike, does it really matter in which order you score the points? I would not think so, so a field goal scored before a touch-down is the same as a field goal after a touch down. Both equals 9 points.Mr. Donhttps://www.blogger.com/profile/03794433688939455277noreply@blogger.comtag:blogger.com,1999:blog-15628310.post-91191825090664349052007-01-23T10:56:00.000-05:002007-01-23T10:56:00.000-05:00I don't think your formula is correct, because you...I don't think your formula is correct, because you cannot score just one point by itself, it has to be combined with a TD.Seandiegohttps://www.blogger.com/profile/10087007318273438928noreply@blogger.comtag:blogger.com,1999:blog-15628310.post-16813268217706713432007-01-23T10:26:00.000-05:002007-01-23T10:26:00.000-05:00Let's build our way up to 20 points (btw, I'm goin...Let's build our way up to 20 points (btw, I'm going to make it a little bit harder and say the order the team scores in counts):<br /><br />There is only one way to get 0 points;<br /><br />There is one way to get 1 point.<br /><br />There is one way to get 2 points<br /><br />There is one way to get 3 points;<br /><br />There is one way to get 4 points (two safeties).<br /><br />When we get to 5 points, we see that this can in two ways, by a safety and a field goal in either order.<br /><br />For 6 points, we could get 3 safeties, or two field goals, or a touchdown.<br /><br />We can get 7 points by 7, or 2+2+3 or 2+3+2 or 3+2+2.<br /><br />We can get 8 points by 2+2+2+2, or (2+3+3, 3+2+3, 3+3+2), or ( 6+2, 2+6 ) or 8.<br /><br />Let's get formulaic from this point on:S(N) = S(N-2) + S(N-3) + S(N-6) + S(N-7) + S(N-8) <br /><br />That is, to get a total score of N, your last score was a 2, 3, 6, 6+1 or 6+2. And the number of ways of getting a score of N is the sum of the number of ways of getting a score that is N-2, N-3, N-6, N-7 or N-8.<br /><br />Our table begins like this:<br />N S(N)<br />0 1<br />1 1<br />2 1<br />3 1<br />4 1<br />5 2<br />6 3<br />7 4<br />8 7<br /><br />Now we can compute new values automatically:<br />N S(N)<br />8 7<br />9 10<br />10 14<br />11 21<br />12 30<br />13 44<br />14 65<br />15 95<br />16 140<br />17 205<br />18 300<br />19 440<br />20 644<br />21 944<br />22 1384<br />23 2028<br />24 2973<br />25 4357<br />26 6385<br />27 9358<br />28 13714<br />29 20099<br />30 29457<br /><br /><br />Note that 20 points can be gotten in 644 ways! <br /><br />As for the Pats loss, it's a shame, but that's the way it goes. I believe mistakes were made and bad calls were made (or not made) by the refs. But that statement applies to both teams, so that in the end, hurray for Indy. I hope the Bears kick their butts! ;-)Anonymoushttps://www.blogger.com/profile/18153935609499338685noreply@blogger.comtag:blogger.com,1999:blog-15628310.post-79326304828953664612007-01-22T21:54:00.000-05:002007-01-22T21:54:00.000-05:001. 2222222222
2. 222222233
3. 22223333
4. 2333333
...1. 2222222222<br />2. 222222233<br />3. 22223333<br />4. 2333333<br />5. 6662<br />6. 662222<br />7. 66332<br />8. 62222222<br />9. 6332222<br />10.633332<br />11.7322222<br />12.733322<br />13.77222<br />14.7733<br />15.776<br />16.76322<br />17.8822<br />18.8732<br />19.86222<br />20.8633<br />21.8222222<br />22.833222<br />23.83333<br /><br />I agreeAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-15628310.post-62607056775201540352007-01-22T21:26:00.000-05:002007-01-22T21:26:00.000-05:00Mike....what was crazy about that game was the pen...Mike....what was crazy about that game was the penalties. They killed the Pats. 12 men in the huddle? Offensive pass interference? They had 4 penalties that came at critical times. Without 2 or 3 of them, Pats win in a blowout.Andyhttps://www.blogger.com/profile/09479999070145487506noreply@blogger.comtag:blogger.com,1999:blog-15628310.post-8677211659048922682007-01-22T19:08:00.000-05:002007-01-22T19:08:00.000-05:00And, for the record, i came up with 23 different s...And, for the record, i came up with 23 different scenarios to make 20 points. I will not list them here, unless requested.<br /><br />GO CHICAGO!!!Mr. Donhttps://www.blogger.com/profile/03794433688939455277noreply@blogger.comtag:blogger.com,1999:blog-15628310.post-51779050434777587422007-01-22T18:19:00.000-05:002007-01-22T18:19:00.000-05:00You could get
2 TDs with the 2 pt conversions and...You could get <br />2 TDs with the 2 pt conversions and 2 safeties.<br /><br />And by the way, GO BEARS!!!!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-15628310.post-71955064679754218742007-01-22T11:27:00.000-05:002007-01-22T11:27:00.000-05:00Yes, I'm a Pats fan. Which is why I'm so cranky t...Yes, I'm a Pats fan. Which is why I'm so cranky today. :-( I think the Colts made just one more play than the Pats did and good for them (sort of... It's hard to be gracious when I'm upset, but I'm trying).Anonymoushttps://www.blogger.com/profile/18153935609499338685noreply@blogger.comtag:blogger.com,1999:blog-15628310.post-28336869196995625792007-01-22T10:20:00.000-05:002007-01-22T10:20:00.000-05:00lots of ways.
3 TDs, 2 extra points and a missed ...lots of ways.<br /><br />3 TDs, 2 extra points and a missed extra point.<br />10 safeties (which will never happen...)<br />6 FGs and a safety<br /><br />etc...<br /><br />Mike are you a Patriots fan? I live in the Boston area myself, although I'm an Eagles fan.Andyhttps://www.blogger.com/profile/09479999070145487506noreply@blogger.com