Mixing
19 people on 8 benches with 1, 2 or 3 people. How many with only 2?
up vote
1
down vote
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I found a math problem for 2nd graders in Norway. The article only presented drawing a table of everything and simply looking at it, instead of a mathematical approach, like a formula. I'm not sure what kind of solution is needed, so I cannot google the type of math needed. It goes like this:
-There are eight benches in a park.
-On each of the benches, there are either 1, 2 or 3 people. So no bench is empty.
-All together there are 19 people on the benches
How many benches have only two people?
The answer is 5:
http://tinyimg.io/i/1SJcOzb.png
Is there a way to figure this out with a formula?
problem-solving
asked 2 days ago
Streching my competence
82
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Streching my competence is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
1
down vote
favorite
I found a math problem for 2nd graders in Norway. The article only presented drawing a table of everything and simply looking at it, instead of a mathematical approach, like a formula. I'm not sure what kind of solution is needed, so I cannot google the type of math needed. It goes like this:
-There are eight benches in a park.
-On each of the benches, there are either 1, 2 or 3 people. So no bench is empty.
-All together there are 19 people on the benches
How many benches have only two people?
The answer is 5:
http://tinyimg.io/i/1SJcOzb.png
Is there a way to figure this out with a formula?
problem-solving
asked 2 days ago
Streching my competence
82
New contributor
Streching my competence is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Why do you say the answer is $5$? If $(a,b,c)$ means there are $a$ benches with one person, $b$ with two, $c$ with three then $(1,3,4),(2,1,5)$ and $(0,5,3)$ all work.
– lulu
2 days ago
This sort of problem is really meant to be played with. Algebraic machinery is going to come down to checking cases (not difficult, but probably not what second graders are going to do).
– lulu
2 days ago
@lulu lol yeah, I just posted the answer they said it was. I of course see now that I can take away one person from any bench with two people and add to another with only two people.
– Streching my competence
2 days ago
Exactly. $quad$
– lulu
2 days ago
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I found a math problem for 2nd graders in Norway. The article only presented drawing a table of everything and simply looking at it, instead of a mathematical approach, like a formula. I'm not sure what kind of solution is needed, so I cannot google the type of math needed. It goes like this:
-There are eight benches in a park.
-On each of the benches, there are either 1, 2 or 3 people. So no bench is empty.
-All together there are 19 people on the benches
How many benches have only two people?
The answer is 5:
http://tinyimg.io/i/1SJcOzb.png
Is there a way to figure this out with a formula?
problem-solving
asked 2 days ago
Streching my competence
82
New contributor
Streching my competence is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I found a math problem for 2nd graders in Norway. The article only presented drawing a table of everything and simply looking at it, instead of a mathematical approach, like a formula. I'm not sure what kind of solution is needed, so I cannot google the type of math needed. It goes like this:
-There are eight benches in a park.
-On each of the benches, there are either 1, 2 or 3 people. So no bench is empty.
-All together there are 19 people on the benches
How many benches have only two people?
The answer is 5:
http://tinyimg.io/i/1SJcOzb.png
Is there a way to figure this out with a formula?
problem-solving
problem-solving
asked 2 days ago
Streching my competence
82
New contributor
Streching my competence is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
Streching my competence
82
New contributor
Streching my competence is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
Streching my competence
82
New contributor
Streching my competence is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
Streching my competence
82
asked 2 days ago
Streching my competence
82
82
New contributor
Streching my competence is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Streching my competence is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Streching my competence is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Why do you say the answer is $5$? If $(a,b,c)$ means there are $a$ benches with one person, $b$ with two, $c$ with three then $(1,3,4),(2,1,5)$ and $(0,5,3)$ all work.
– lulu
2 days ago
This sort of problem is really meant to be played with. Algebraic machinery is going to come down to checking cases (not difficult, but probably not what second graders are going to do).
– lulu
2 days ago
@lulu lol yeah, I just posted the answer they said it was. I of course see now that I can take away one person from any bench with two people and add to another with only two people.
– Streching my competence
2 days ago
Exactly. $quad$
– lulu
2 days ago
add a comment |
Why do you say the answer is $5$? If $(a,b,c)$ means there are $a$ benches with one person, $b$ with two, $c$ with three then $(1,3,4),(2,1,5)$ and $(0,5,3)$ all work.
– lulu
2 days ago
This sort of problem is really meant to be played with. Algebraic machinery is going to come down to checking cases (not difficult, but probably not what second graders are going to do).
– lulu
2 days ago
@lulu lol yeah, I just posted the answer they said it was. I of course see now that I can take away one person from any bench with two people and add to another with only two people.
– Streching my competence
2 days ago
Exactly. $quad$
– lulu
2 days ago
Why do you say the answer is $5$? If $(a,b,c)$ means there are $a$ benches with one person, $b$ with two, $c$ with three then $(1,3,4),(2,1,5)$ and $(0,5,3)$ all work.
– lulu
2 days ago
Why do you say the answer is $5$? If $(a,b,c)$ means there are $a$ benches with one person, $b$ with two, $c$ with three then $(1,3,4),(2,1,5)$ and $(0,5,3)$ all work.
– lulu
2 days ago
This sort of problem is really meant to be played with. Algebraic machinery is going to come down to checking cases (not difficult, but probably not what second graders are going to do).
– lulu
2 days ago
This sort of problem is really meant to be played with. Algebraic machinery is going to come down to checking cases (not difficult, but probably not what second graders are going to do).
– lulu
2 days ago
@lulu lol yeah, I just posted the answer they said it was. I of course see now that I can take away one person from any bench with two people and add to another with only two people.
– Streching my competence
2 days ago
@lulu lol yeah, I just posted the answer they said it was. I of course see now that I can take away one person from any bench with two people and add to another with only two people.
– Streching my competence
2 days ago
Exactly. $quad$
– lulu
2 days ago
Exactly. $quad$
– lulu
2 days ago
add a comment |
2 Answers
2
active
oldest
votes
up vote
1
down vote
accepted
If there are $x$ benches with one person, $y$ with two and $z$ with three then you have the simultaneous equations $$x+y+z=8$$ $$x+2y+3z=19$$
You can eliminate one term to give (depending on which is eliminated)$$y +2x = 5$$ $$y+2z=11$$ $$z-x=3$$
so if $x,y,z$ are non negative integers, then from the first of these $x$ can only be any of $0,1,2$, requiring $z=3,4,5$ and $y=5,3,1$ respectively
answered 2 days ago
Henry
96.6k474154
This is more than an American 2nd grader would be able to handle. I can't speak to Norway, but I bet they're waaay smarter. ;-)
– Russ
2 days ago
1
Amazing! Thanks. @Russ: Haha, I doubt it. I believe they don't start with theoretical math until university, to my understanding from the article mentioning that text based problems in such low grades are a problem. I know for a fact they don't in Sweden at least, as one of my math teachers in 12th grade math explained that it's an issue in Sweden and that this harms kids ability to learn in other subjects too, and that it's pretty unique compared to the rest of the world. Sweden and Norway are very similar.
– Streching my competence
2 days ago
@Strechingmycompetence it varies in the U.S. In the DC area, many schools participate in Math Olympiads, and problems similar to this might be presented to 4th or 5th graders: "how many ways are there to arrange 19 people into 8 benches such that ..." They would not check the work on this, only the answer, but they would review the problem with the class afterward. However, Math Olypiad is optional for most, and usually is given to the advanced students that go to a special class instead of the usual math class.
– Russ
yesterday
add a comment |
up vote
0
down vote
But it's not true as the problem is stated. The stated solution is listed as
begin{array}{r|cccccccc|}
text{Benches} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8\
hline
& bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc & bigcirc & bigcirc \
text{people} & bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc & bigcirc & bigcirc \
& bigcirc & bigcirc & bigcirc \
hline
end{array}
And there are five benches with only two people.
But what is wrong with this answer?
begin{array}{r|cccccccc|}
text{Benches} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8\
hline
& bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc & bigcirc & bigcirc \
text{people} & bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc & bigcirc\
& bigcirc & bigcirc & bigcirc & bigcirc \
hline
end{array}
Or this answer?
begin{array}{r|cccccccc|}
text{Benches} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8\
hline
& bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc & bigcirc & bigcirc \
text{people} & bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc \
& bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc\
hline
end{array}
answered 2 days ago
steven gregory
17.4k22156
True. I just took the presented answer as the sole truth, which wasn't particularly smart in hindsight. Does the multiple possible answers mean there is no way to draw up a formula for a solution, or any of them?
– Streching my competence
2 days ago
What you are talking about is a restricted partition. It's not a simple subject to study.
– steven gregory
2 days ago
1
Holy moly! I'll leave that there. I'd upvote you for your effort but sadly this site won't allow me being that I'm too fresh /:
– Streching my competence
2 days ago
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
If there are $x$ benches with one person, $y$ with two and $z$ with three then you have the simultaneous equations $$x+y+z=8$$ $$x+2y+3z=19$$
You can eliminate one term to give (depending on which is eliminated)$$y +2x = 5$$ $$y+2z=11$$ $$z-x=3$$
so if $x,y,z$ are non negative integers, then from the first of these $x$ can only be any of $0,1,2$, requiring $z=3,4,5$ and $y=5,3,1$ respectively
answered 2 days ago
Henry
96.6k474154
This is more than an American 2nd grader would be able to handle. I can't speak to Norway, but I bet they're waaay smarter. ;-)
– Russ
2 days ago
1
Amazing! Thanks. @Russ: Haha, I doubt it. I believe they don't start with theoretical math until university, to my understanding from the article mentioning that text based problems in such low grades are a problem. I know for a fact they don't in Sweden at least, as one of my math teachers in 12th grade math explained that it's an issue in Sweden and that this harms kids ability to learn in other subjects too, and that it's pretty unique compared to the rest of the world. Sweden and Norway are very similar.
– Streching my competence
2 days ago
@Strechingmycompetence it varies in the U.S. In the DC area, many schools participate in Math Olympiads, and problems similar to this might be presented to 4th or 5th graders: "how many ways are there to arrange 19 people into 8 benches such that ..." They would not check the work on this, only the answer, but they would review the problem with the class afterward. However, Math Olypiad is optional for most, and usually is given to the advanced students that go to a special class instead of the usual math class.
– Russ
yesterday
add a comment |
up vote
1
down vote
accepted
If there are $x$ benches with one person, $y$ with two and $z$ with three then you have the simultaneous equations $$x+y+z=8$$ $$x+2y+3z=19$$
You can eliminate one term to give (depending on which is eliminated)$$y +2x = 5$$ $$y+2z=11$$ $$z-x=3$$
so if $x,y,z$ are non negative integers, then from the first of these $x$ can only be any of $0,1,2$, requiring $z=3,4,5$ and $y=5,3,1$ respectively
answered 2 days ago
Henry
96.6k474154
This is more than an American 2nd grader would be able to handle. I can't speak to Norway, but I bet they're waaay smarter. ;-)
– Russ
2 days ago
1
Amazing! Thanks. @Russ: Haha, I doubt it. I believe they don't start with theoretical math until university, to my understanding from the article mentioning that text based problems in such low grades are a problem. I know for a fact they don't in Sweden at least, as one of my math teachers in 12th grade math explained that it's an issue in Sweden and that this harms kids ability to learn in other subjects too, and that it's pretty unique compared to the rest of the world. Sweden and Norway are very similar.
– Streching my competence
2 days ago
@Strechingmycompetence it varies in the U.S. In the DC area, many schools participate in Math Olympiads, and problems similar to this might be presented to 4th or 5th graders: "how many ways are there to arrange 19 people into 8 benches such that ..." They would not check the work on this, only the answer, but they would review the problem with the class afterward. However, Math Olypiad is optional for most, and usually is given to the advanced students that go to a special class instead of the usual math class.
– Russ
yesterday
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
If there are $x$ benches with one person, $y$ with two and $z$ with three then you have the simultaneous equations $$x+y+z=8$$ $$x+2y+3z=19$$
You can eliminate one term to give (depending on which is eliminated)$$y +2x = 5$$ $$y+2z=11$$ $$z-x=3$$
so if $x,y,z$ are non negative integers, then from the first of these $x$ can only be any of $0,1,2$, requiring $z=3,4,5$ and $y=5,3,1$ respectively
answered 2 days ago
Henry
96.6k474154
If there are $x$ benches with one person, $y$ with two and $z$ with three then you have the simultaneous equations $$x+y+z=8$$ $$x+2y+3z=19$$
You can eliminate one term to give (depending on which is eliminated)$$y +2x = 5$$ $$y+2z=11$$ $$z-x=3$$
so if $x,y,z$ are non negative integers, then from the first of these $x$ can only be any of $0,1,2$, requiring $z=3,4,5$ and $y=5,3,1$ respectively
answered 2 days ago
Henry
96.6k474154
answered 2 days ago
Henry
96.6k474154
answered 2 days ago
Henry
96.6k474154
answered 2 days ago
Henry
96.6k474154
96.6k474154
This is more than an American 2nd grader would be able to handle. I can't speak to Norway, but I bet they're waaay smarter. ;-)
– Russ
2 days ago
1
Amazing! Thanks. @Russ: Haha, I doubt it. I believe they don't start with theoretical math until university, to my understanding from the article mentioning that text based problems in such low grades are a problem. I know for a fact they don't in Sweden at least, as one of my math teachers in 12th grade math explained that it's an issue in Sweden and that this harms kids ability to learn in other subjects too, and that it's pretty unique compared to the rest of the world. Sweden and Norway are very similar.
– Streching my competence
2 days ago
@Strechingmycompetence it varies in the U.S. In the DC area, many schools participate in Math Olympiads, and problems similar to this might be presented to 4th or 5th graders: "how many ways are there to arrange 19 people into 8 benches such that ..." They would not check the work on this, only the answer, but they would review the problem with the class afterward. However, Math Olypiad is optional for most, and usually is given to the advanced students that go to a special class instead of the usual math class.
– Russ
yesterday
add a comment |
This is more than an American 2nd grader would be able to handle. I can't speak to Norway, but I bet they're waaay smarter. ;-)
– Russ
2 days ago
1
Amazing! Thanks. @Russ: Haha, I doubt it. I believe they don't start with theoretical math until university, to my understanding from the article mentioning that text based problems in such low grades are a problem. I know for a fact they don't in Sweden at least, as one of my math teachers in 12th grade math explained that it's an issue in Sweden and that this harms kids ability to learn in other subjects too, and that it's pretty unique compared to the rest of the world. Sweden and Norway are very similar.
– Streching my competence
2 days ago
@Strechingmycompetence it varies in the U.S. In the DC area, many schools participate in Math Olympiads, and problems similar to this might be presented to 4th or 5th graders: "how many ways are there to arrange 19 people into 8 benches such that ..." They would not check the work on this, only the answer, but they would review the problem with the class afterward. However, Math Olypiad is optional for most, and usually is given to the advanced students that go to a special class instead of the usual math class.
– Russ
yesterday
This is more than an American 2nd grader would be able to handle. I can't speak to Norway, but I bet they're waaay smarter. ;-)
– Russ
2 days ago
This is more than an American 2nd grader would be able to handle. I can't speak to Norway, but I bet they're waaay smarter. ;-)
– Russ
2 days ago
1
1
Amazing! Thanks. @Russ: Haha, I doubt it. I believe they don't start with theoretical math until university, to my understanding from the article mentioning that text based problems in such low grades are a problem. I know for a fact they don't in Sweden at least, as one of my math teachers in 12th grade math explained that it's an issue in Sweden and that this harms kids ability to learn in other subjects too, and that it's pretty unique compared to the rest of the world. Sweden and Norway are very similar.
– Streching my competence
2 days ago
Amazing! Thanks. @Russ: Haha, I doubt it. I believe they don't start with theoretical math until university, to my understanding from the article mentioning that text based problems in such low grades are a problem. I know for a fact they don't in Sweden at least, as one of my math teachers in 12th grade math explained that it's an issue in Sweden and that this harms kids ability to learn in other subjects too, and that it's pretty unique compared to the rest of the world. Sweden and Norway are very similar.
– Streching my competence
2 days ago
@Strechingmycompetence it varies in the U.S. In the DC area, many schools participate in Math Olympiads, and problems similar to this might be presented to 4th or 5th graders: "how many ways are there to arrange 19 people into 8 benches such that ..." They would not check the work on this, only the answer, but they would review the problem with the class afterward. However, Math Olypiad is optional for most, and usually is given to the advanced students that go to a special class instead of the usual math class.
– Russ
yesterday
@Strechingmycompetence it varies in the U.S. In the DC area, many schools participate in Math Olympiads, and problems similar to this might be presented to 4th or 5th graders: "how many ways are there to arrange 19 people into 8 benches such that ..." They would not check the work on this, only the answer, but they would review the problem with the class afterward. However, Math Olypiad is optional for most, and usually is given to the advanced students that go to a special class instead of the usual math class.
– Russ
yesterday
add a comment |
up vote
0
down vote
But it's not true as the problem is stated. The stated solution is listed as
begin{array}{r|cccccccc|}
text{Benches} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8\
hline
& bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc & bigcirc & bigcirc \
text{people} & bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc & bigcirc & bigcirc \
& bigcirc & bigcirc & bigcirc \
hline
end{array}
And there are five benches with only two people.
But what is wrong with this answer?
begin{array}{r|cccccccc|}
text{Benches} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8\
hline
& bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc & bigcirc & bigcirc \
text{people} & bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc & bigcirc\
& bigcirc & bigcirc & bigcirc & bigcirc \
hline
end{array}
Or this answer?
begin{array}{r|cccccccc|}
text{Benches} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8\
hline
& bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc & bigcirc & bigcirc \
text{people} & bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc \
& bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc\
hline
end{array}
answered 2 days ago
steven gregory
17.4k22156
True. I just took the presented answer as the sole truth, which wasn't particularly smart in hindsight. Does the multiple possible answers mean there is no way to draw up a formula for a solution, or any of them?
– Streching my competence
2 days ago
What you are talking about is a restricted partition. It's not a simple subject to study.
– steven gregory
2 days ago
1
Holy moly! I'll leave that there. I'd upvote you for your effort but sadly this site won't allow me being that I'm too fresh /:
– Streching my competence
2 days ago
add a comment |
up vote
0
down vote
But it's not true as the problem is stated. The stated solution is listed as
begin{array}{r|cccccccc|}
text{Benches} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8\
hline
& bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc & bigcirc & bigcirc \
text{people} & bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc & bigcirc & bigcirc \
& bigcirc & bigcirc & bigcirc \
hline
end{array}
And there are five benches with only two people.
But what is wrong with this answer?
begin{array}{r|cccccccc|}
text{Benches} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8\
hline
& bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc & bigcirc & bigcirc \
text{people} & bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc & bigcirc\
& bigcirc & bigcirc & bigcirc & bigcirc \
hline
end{array}
Or this answer?
begin{array}{r|cccccccc|}
text{Benches} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8\
hline
& bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc & bigcirc & bigcirc \
text{people} & bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc \
& bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc\
hline
end{array}
answered 2 days ago
steven gregory
17.4k22156
True. I just took the presented answer as the sole truth, which wasn't particularly smart in hindsight. Does the multiple possible answers mean there is no way to draw up a formula for a solution, or any of them?
– Streching my competence
2 days ago
What you are talking about is a restricted partition. It's not a simple subject to study.
– steven gregory
2 days ago
1
Holy moly! I'll leave that there. I'd upvote you for your effort but sadly this site won't allow me being that I'm too fresh /:
– Streching my competence
2 days ago
add a comment |
up vote
0
down vote
up vote
0
down vote
But it's not true as the problem is stated. The stated solution is listed as
begin{array}{r|cccccccc|}
text{Benches} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8\
hline
& bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc & bigcirc & bigcirc \
text{people} & bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc & bigcirc & bigcirc \
& bigcirc & bigcirc & bigcirc \
hline
end{array}
And there are five benches with only two people.
But what is wrong with this answer?
begin{array}{r|cccccccc|}
text{Benches} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8\
hline
& bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc & bigcirc & bigcirc \
text{people} & bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc & bigcirc\
& bigcirc & bigcirc & bigcirc & bigcirc \
hline
end{array}
Or this answer?
begin{array}{r|cccccccc|}
text{Benches} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8\
hline
& bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc & bigcirc & bigcirc \
text{people} & bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc \
& bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc\
hline
end{array}
answered 2 days ago
steven gregory
17.4k22156
But it's not true as the problem is stated. The stated solution is listed as
begin{array}{r|cccccccc|}
text{Benches} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8\
hline
& bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc & bigcirc & bigcirc \
text{people} & bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc & bigcirc & bigcirc \
& bigcirc & bigcirc & bigcirc \
hline
end{array}
And there are five benches with only two people.
But what is wrong with this answer?
begin{array}{r|cccccccc|}
text{Benches} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8\
hline
& bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc & bigcirc & bigcirc \
text{people} & bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc & bigcirc\
& bigcirc & bigcirc & bigcirc & bigcirc \
hline
end{array}
Or this answer?
begin{array}{r|cccccccc|}
text{Benches} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8\
hline
& bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc & bigcirc & bigcirc \
text{people} & bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc & bigcirc \
& bigcirc & bigcirc & bigcirc & bigcirc
& bigcirc\
hline
end{array}
answered 2 days ago
steven gregory
17.4k22156
answered 2 days ago
steven gregory
17.4k22156
answered 2 days ago
steven gregory
17.4k22156
answered 2 days ago
steven gregory
17.4k22156
17.4k22156
True. I just took the presented answer as the sole truth, which wasn't particularly smart in hindsight. Does the multiple possible answers mean there is no way to draw up a formula for a solution, or any of them?
– Streching my competence
2 days ago
What you are talking about is a restricted partition. It's not a simple subject to study.
– steven gregory
2 days ago
1
Holy moly! I'll leave that there. I'd upvote you for your effort but sadly this site won't allow me being that I'm too fresh /:
– Streching my competence
2 days ago
add a comment |
True. I just took the presented answer as the sole truth, which wasn't particularly smart in hindsight. Does the multiple possible answers mean there is no way to draw up a formula for a solution, or any of them?
– Streching my competence
2 days ago
What you are talking about is a restricted partition. It's not a simple subject to study.
– steven gregory
2 days ago
1
Holy moly! I'll leave that there. I'd upvote you for your effort but sadly this site won't allow me being that I'm too fresh /:
– Streching my competence
2 days ago
True. I just took the presented answer as the sole truth, which wasn't particularly smart in hindsight. Does the multiple possible answers mean there is no way to draw up a formula for a solution, or any of them?
– Streching my competence
2 days ago
True. I just took the presented answer as the sole truth, which wasn't particularly smart in hindsight. Does the multiple possible answers mean there is no way to draw up a formula for a solution, or any of them?
– Streching my competence
2 days ago
What you are talking about is a restricted partition. It's not a simple subject to study.
– steven gregory
2 days ago
What you are talking about is a restricted partition. It's not a simple subject to study.
– steven gregory
2 days ago
1
1
Holy moly! I'll leave that there. I'd upvote you for your effort but sadly this site won't allow me being that I'm too fresh /:
– Streching my competence
2 days ago
Holy moly! I'll leave that there. I'd upvote you for your effort but sadly this site won't allow me being that I'm too fresh /:
– Streching my competence
2 days ago
add a comment |
Streching my competence is a new contributor. Be nice, and check out our Code of Conduct.
Streching my competence is a new contributor. Be nice, and check out our Code of Conduct.
Streching my competence is a new contributor. Be nice, and check out our Code of Conduct.
Streching my competence is a new contributor. Be nice, and check out our Code of Conduct.
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Why do you say the answer is $5$? If $(a,b,c)$ means there are $a$ benches with one person, $b$ with two, $c$ with three then $(1,3,4),(2,1,5)$ and $(0,5,3)$ all work.
– lulu
2 days ago
This sort of problem is really meant to be played with. Algebraic machinery is going to come down to checking cases (not difficult, but probably not what second graders are going to do).
– lulu
2 days ago
@lulu lol yeah, I just posted the answer they said it was. I of course see now that I can take away one person from any bench with two people and add to another with only two people.
– Streching my competence
2 days ago
Exactly. $quad$
– lulu
2 days ago