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A114143
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The possible sums of the final scores of completed Chicago Bears football games where both teams score.
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0
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4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| 1 point only is an impossible score in American football. But with the safety 2 and the field goal 3, we can construct the set of integers greater than 1. We can prove this by noting that if a score is even, we can build it with a series of safeties. Of course the other scorings allowed of 3,6 and 1 after a touchdown, could also be used. Now if a score is odd it is of the form 2k+3. So for any odd number 2m+1, we subtract 3 or 1 field goal from it to make it even and divide by 2 to get the number of safeties we need to add back to the field goal. Symbolically, let the odd number be 2m+1. then (2m+1 - 3)/2 = m-1 safeties needed. Add this to 3 and you will have the number. For example, say we want a score of 99. 99 = 2m+1 and m = 49. So m-1 = 48 safeties + 1 field goal = 99 points. From the first statement that 1 is an impossible score, it follows there is an infinite number of impossible scores in football. Ie., 1,0 1,1 1,2 1,3 ... Moreover, this restriction greatly influences the outcome of the ending digits for match up to the 100 square game cards rhat are floating around throughout the World before the Super Bowl game.
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LINKS
| Tanya Khovanova, Non Recursions
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EXAMPLE
| A safety or 2 points is the minimum possible score at the end of a game. So if
two teams score one safety each, the sum of their scores will be 4. The next
number 5 is a safety for one team and a field goal for the other.
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CROSSREFS
| Sequence in context: A089166 A178052 A030543 * A171526 A171463 A020705
Adjacent sequences: A114140 A114141 A114142 * A114144 A114145 A114146
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KEYWORD
| easy,nonn
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AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), Feb 03 2006
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