Posted: 12/8/2015 8:50:12 PM EDT
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Kids got a math problem...maybe I am reading into this too much,.,,but I (and him) are drawing a blank.
Organized list "Two teams decide a touchdown is worth 5 points and a field goal is worth 3 points. What is the highest score a team CANNOT reach with any combination of touchdowns and field goals?" I am sure I am overthinking this...but wouldn't it be infinity? |
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Kids got a math problem...maybe I am reading into this too much,.,,but I (and him) are drawing a blank. Organized list "Two teams decide a touchdown is worth 5 points and a field goal is worth 3 points. What is the highest score a team CANNOT reach with any combination of touchdowns and field goals?" I am sure I am overthinking this...but wouldn't it be infinity? Makes sense to me. Prime numbers... |
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FOUR? |
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Makes sense to me. Prime numbers... Quoted:
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Kids got a math problem...maybe I am reading into this too much,.,,but I (and him) are drawing a blank. Organized list "Two teams decide a touchdown is worth 5 points and a field goal is worth 3 points. What is the highest score a team CANNOT reach with any combination of touchdowns and field goals?" I am sure I am overthinking this...but wouldn't it be infinity? Makes sense to me. Prime numbers... This leaves out the additive part. Not that I know much more than that. 288 - 3 = 285 and 285 is divisible by 5 so that doesn't pass. |
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Quoted: Kids got a math problem...maybe I am reading into this too much,.,,but I (and him) are drawing a blank. Organized list "Two teams decide a touchdown is worth 5 points and a field goal is worth 3 points. What is the highest score a team CANNOT reach with any combination of touchdowns and field goals?" I am sure I am overthinking this...but wouldn't it be infinity? As the final scores go up, you have an ever increasing variety of TDs and FGs to work with (unless it's the Bears you are talking about) to make the number. 1,2,4 are all "cannot be reached" numbers. 5 is one TD. 6 is two FGs. 7 cannot be reached. 8 can be reached with one of each. Keep going like that until you have a handful of each for the math. I have no idea how one would show work for this. The kid should know some techniques that they have been teaching in whatever bullshit methods of math they are teaching at the school. |
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Assume that the game lasts 4 15min quarters or 1 hr.
Assume the average running speed is 8 mph. A team, assuming no fatigue, will then run 8 miles in the one game. Assuming that the kickoff return runs endzone to end zone for one play, and then the opponent turns over the ball and start again so that one team always has possession of the ball (say, interceptions fumbles etc.). 8 miles is 14080 yds, so a team can make 140.80 possible scores. or 140. so max score in 1 game is 5*140 =700 points. That's your hard limit. not infinity. any number that ends in 5 or 0 is divisible by 5. a number is divisible by 3 if the sum of the digits is evenly divisible by 3. (e.g. 123 > 1+2+3 = 6 which is div.by3., 556 > 5+5+6 = 16 which is not evenly div. by 3) A number is divisible by 8 if the number represented by its last three digits is divisible by 8. Running this through Matlab for the scores of 650 to 700, the highest number that is not divisible by 3,5 or 8 is 698. Thus, based on the assumptions made, your answer is 698. or brute force: 0,3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,58...i+3, where i=1,2...140 0, 5,10,15,20,25,30,35,40,45,50,55,60,...i+5, where i=1,2...140 0,8,16,24,32,40,48,56,64,...i+8, where i=1,2...140 Missing:1,2,4,7,11,13,14,17 I think you might need more information or check out http://primes.utm.edu/largest.html largest prime is: prime=2^(57885161)-1 digits =17425170 reference=Mersenne 48?? |
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Assume that the game lasts 4 15min quarters or 1 hr. Assume the average running speed is 8 mph. A team, assuming no fatigue, will then run 8 miles in the one game. Assuming that the kickoff return runs endzone to end zone for one play, and then the opponent turns over the ball and start again so that one team always has possession of the ball (say, interceptions fumbles etc.). 8 miles is 14080 yds, so a team can make 140.80 possible scores. or 140. so max score in 1 game is 5*140 =700 points. That's your hard limit. not infinity. any number that ends in 5 or 0 is divisible by 5. a number is divisible by 3 if the sum of the digits is evenly divisible by 3. (e.g. 123 > 1+2+3 = 6 which is div.by3., 556 > 5+5+6 = 16 which is not evenly div. by 3) A number is divisible by 8 if the number represented by its last three digits is divisible by 8. Running this through Matlab for the scores of 650 to 700, the highest number that is not divisible by 3,5 or 8 is 698. Thus, based on the assumptions made, your answer is 698. or brute force: 0,3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,58...i+3, where i=1,2...140 0, 5,10,15,20,25,30,35,40,45,50,55,60,...i+5, where i=1,2...140 0,8,16,24,32,40,48,56,64,...i+8, where i=1,2...140 Missing:1,2,4,7,11,13,14,17 I think you might need more information or check out http://primes.utm.edu/largest.html largest prime is: prime=2^(57885161)-1 digits =17425170 reference=Mersenne 48??  
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Running this through Matlab for the scores of 650 to 700, the highest number that is not divisible by 3,5 or 8 is 698. Thus, based on the assumptions made, your answer is 698. A fuuuuuccccckkkkkload of touchdowns equals 695. Plus a game ending field goal is 698 
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anything that's not divisible by 3, 5, 8 so maybe 3 x 5 x 8 + 1 or 121 Nope: 20 touchdowns and 7 field goals 100 points + 21 points = 121 points. It is also not the largest known prime since we aren't looking at dividing by just one integer. Instead, we have a sum of two values, each with an unknown product. If you just solve for integers 1 through 20, you will see we can achieve almost any value with the exception of 1, 2, 4, and 7. 1- 2- 3 - 1x3 4 - 5 - 1x5 6 - 2x3 7 - 8 - 1x5 + 1x3 9 - 3x3 10 - 2x5 11 - 1x5 + 2x3 12 - 4x3 13 - 2x5 + 1x3 14 - 1x5 + 3x3 15 - 3x5 16 - 2x5 + 2x3 17 - 1x5 + 4x3 18 - 6x3 19 - 2x5 + 3x3 20 - 4x5 You can add up the values we have solved for to yield any number above 20, so the answer is 7. |
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Assume that the game lasts 4 15min quarters or 1 hr. Assume the average running speed is 8 mph. A team, assuming no fatigue, will then run 8 miles in the one game. Assuming that the kickoff return runs endzone to end zone for one play, and then the opponent turns over the ball and start again so that one team always has possession of the ball (say, interceptions fumbles etc.). 8 miles is 14080 yds, so a team can make 140.80 possible scores. or 140. so max score in 1 game is 5*140 =700 points. That's your hard limit. not infinity. any number that ends in 5 or 0 is divisible by 5. a number is divisible by 3 if the sum of the digits is evenly divisible by 3. (e.g. 123 > 1+2+3 = 6 which is div.by3., 556 > 5+5+6 = 16 which is not evenly div. by 3) A number is divisible by 8 if the number represented by its last three digits is divisible by 8. Running this through Matlab for the scores of 650 to 700, the highest number that is not divisible by 3,5 or 8 is 698. Thus, based on the assumptions made, your answer is 698. or brute force: 0,3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,58...i+3, where i=1,2...140 0, 5,10,15,20,25,30,35,40,45,50,55,60,...i+5, where i=1,2...140 0,8,16,24,32,40,48,56,64,...i+8, where i=1,2...140 Missing:1,2,4,7,11,13,14,17 I think you might need more information or check out http://primes.utm.edu/largest.html largest prime is: prime=2^(57885161)-1 digits =17425170 reference=Mersenne 48?? are you an asian wizard? |
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Running this through Matlab for the scores of 650 to 700, the highest number that is not divisible by 3,5 or 8 is 698. <snip> We're not looking for numbers divisible by 3, 5 or 8. We need a number not divisible by 3a + 5b, where a and b are positive integers. 
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This leaves out the additive part. Not that I know much more than that. 288 - 3 = 285 and 285 is divisible by 5 so that doesn't pass. Quoted:
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Kids got a math problem...maybe I am reading into this too much,.,,but I (and him) are drawing a blank. Organized list "Two teams decide a touchdown is worth 5 points and a field goal is worth 3 points. What is the highest score a team CANNOT reach with any combination of touchdowns and field goals?" I am sure I am overthinking this...but wouldn't it be infinity? Makes sense to me. Prime numbers... This leaves out the additive part. Not that I know much more than that. 288 - 3 = 285 and 285 is divisible by 5 so that doesn't pass. Doh. I was thinking multiplication. 
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