In a 7x7 grid, what is the number in the bottom right corner?
up vote
4
down vote
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My math teacher have presented me with a problem, that in my opinion is quite hard. It goes.
"You have a 7x7 grid. Some of the spaces in the grid are already filled with numbers. You have to insert numbers in the remaining spaces, so that the sum in every 3x3 grid inside the 7x7, is 2019. What number should be in the bottom right corner?"
Here is the grid.
I know the answer is 7, but I have no idea of how you arrive at that answer.
analysis pattern-recognition
asked Nov 24 at 9:30
Carl
286
add a comment |
up vote
4
down vote
favorite
My math teacher have presented me with a problem, that in my opinion is quite hard. It goes.
"You have a 7x7 grid. Some of the spaces in the grid are already filled with numbers. You have to insert numbers in the remaining spaces, so that the sum in every 3x3 grid inside the 7x7, is 2019. What number should be in the bottom right corner?"
Here is the grid.
I know the answer is 7, but I have no idea of how you arrive at that answer.
analysis pattern-recognition
asked Nov 24 at 9:30
Carl
286
1
Hint: Fill in as many zeroes as you can, until you are forced to put a number to make the total sum of the grid $2019$.
– Toby Mak
Nov 24 at 10:06
Also, are you sure the number in the top right corner is correct?
– Toby Mak
Nov 24 at 10:12
Cool, I will try using that strategy. That picture came with the problem, so I must assume it is correct.
– Carl
Nov 24 at 10:16
add a comment |
up vote
4
down vote
favorite
up vote
4
down vote
favorite
My math teacher have presented me with a problem, that in my opinion is quite hard. It goes.
"You have a 7x7 grid. Some of the spaces in the grid are already filled with numbers. You have to insert numbers in the remaining spaces, so that the sum in every 3x3 grid inside the 7x7, is 2019. What number should be in the bottom right corner?"
Here is the grid.
I know the answer is 7, but I have no idea of how you arrive at that answer.
analysis pattern-recognition
asked Nov 24 at 9:30
Carl
286
My math teacher have presented me with a problem, that in my opinion is quite hard. It goes.
"You have a 7x7 grid. Some of the spaces in the grid are already filled with numbers. You have to insert numbers in the remaining spaces, so that the sum in every 3x3 grid inside the 7x7, is 2019. What number should be in the bottom right corner?"
Here is the grid.
I know the answer is 7, but I have no idea of how you arrive at that answer.
analysis pattern-recognition
analysis pattern-recognition
asked Nov 24 at 9:30
Carl
286
asked Nov 24 at 9:30
Carl
286
asked Nov 24 at 9:30
Carl
286
asked Nov 24 at 9:30
Carl
286
asked Nov 24 at 9:30
Carl
286
286
1
Hint: Fill in as many zeroes as you can, until you are forced to put a number to make the total sum of the grid $2019$.
– Toby Mak
Nov 24 at 10:06
Also, are you sure the number in the top right corner is correct?
– Toby Mak
Nov 24 at 10:12
Cool, I will try using that strategy. That picture came with the problem, so I must assume it is correct.
– Carl
Nov 24 at 10:16
add a comment |
1
Hint: Fill in as many zeroes as you can, until you are forced to put a number to make the total sum of the grid $2019$.
– Toby Mak
Nov 24 at 10:06
Also, are you sure the number in the top right corner is correct?
– Toby Mak
Nov 24 at 10:12
Cool, I will try using that strategy. That picture came with the problem, so I must assume it is correct.
– Carl
Nov 24 at 10:16
1
1
Hint: Fill in as many zeroes as you can, until you are forced to put a number to make the total sum of the grid $2019$.
– Toby Mak
Nov 24 at 10:06
Hint: Fill in as many zeroes as you can, until you are forced to put a number to make the total sum of the grid $2019$.
– Toby Mak
Nov 24 at 10:06
Also, are you sure the number in the top right corner is correct?
– Toby Mak
Nov 24 at 10:12
Also, are you sure the number in the top right corner is correct?
– Toby Mak
Nov 24 at 10:12
Cool, I will try using that strategy. That picture came with the problem, so I must assume it is correct.
– Carl
Nov 24 at 10:16
Cool, I will try using that strategy. That picture came with the problem, so I must assume it is correct.
– Carl
Nov 24 at 10:16
add a comment |
1 Answer
1
active
oldest
votes
up vote
1
down vote
accepted
Hint: fill in the sums in the boxes such that every 3x3 sub grid has the same sum.
begin{array}{|ccccc|}
hline
10 & boxed{a+b} & 8 & boxed{c+d} & 11 \
\
\
7 & boxed{phantom{0quad 0}} & boxed{phantom 0} & boxed{phantom{0quad 0}} & boxed{phantom 0} \
\
\
6 & boxed{phantom{0quad 0}} & boxed{phantom 0} & boxed{phantom{0quad 0}} & boxed{phantom 0} \
hline
end{array}
answered Nov 24 at 13:58
I like Serena
3,4871718
How would I know sum to start with? Should I for instance say a= 15 b=20, and then work my way down?
– Carl
Nov 24 at 17:01
You could do that. But I intended to leave them as is. So for instance the first empty rectangle must contain $a+b+10-7$ to ensure the 3x3 sub grid has the same sum.
– I like Serena
Nov 24 at 17:14
Yeah okay now I see. But what should I then put inside the square next to the rectangle. Just an 8 as the square above it?
– Carl
Nov 24 at 17:27
If we shift the top left square a row down, we lose $10+a+b$, and gain $7$ plus an unknown sum. Therefore that unknown sum must be $a+b+3$. If we shift the square with $a+b,8$ a row down, we lose $a+b+8$, and gain $a+b+3$ plus the unknown square. Therefore the unknown square must be $5$.
– I like Serena
Nov 24 at 18:33
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
Hint: fill in the sums in the boxes such that every 3x3 sub grid has the same sum.
begin{array}{|ccccc|}
hline
10 & boxed{a+b} & 8 & boxed{c+d} & 11 \
\
\
7 & boxed{phantom{0quad 0}} & boxed{phantom 0} & boxed{phantom{0quad 0}} & boxed{phantom 0} \
\
\
6 & boxed{phantom{0quad 0}} & boxed{phantom 0} & boxed{phantom{0quad 0}} & boxed{phantom 0} \
hline
end{array}
answered Nov 24 at 13:58
I like Serena
3,4871718
How would I know sum to start with? Should I for instance say a= 15 b=20, and then work my way down?
– Carl
Nov 24 at 17:01
You could do that. But I intended to leave them as is. So for instance the first empty rectangle must contain $a+b+10-7$ to ensure the 3x3 sub grid has the same sum.
– I like Serena
Nov 24 at 17:14
Yeah okay now I see. But what should I then put inside the square next to the rectangle. Just an 8 as the square above it?
– Carl
Nov 24 at 17:27
If we shift the top left square a row down, we lose $10+a+b$, and gain $7$ plus an unknown sum. Therefore that unknown sum must be $a+b+3$. If we shift the square with $a+b,8$ a row down, we lose $a+b+8$, and gain $a+b+3$ plus the unknown square. Therefore the unknown square must be $5$.
– I like Serena
Nov 24 at 18:33
add a comment |
up vote
1
down vote
accepted
Hint: fill in the sums in the boxes such that every 3x3 sub grid has the same sum.
begin{array}{|ccccc|}
hline
10 & boxed{a+b} & 8 & boxed{c+d} & 11 \
\
\
7 & boxed{phantom{0quad 0}} & boxed{phantom 0} & boxed{phantom{0quad 0}} & boxed{phantom 0} \
\
\
6 & boxed{phantom{0quad 0}} & boxed{phantom 0} & boxed{phantom{0quad 0}} & boxed{phantom 0} \
hline
end{array}
answered Nov 24 at 13:58
I like Serena
3,4871718
How would I know sum to start with? Should I for instance say a= 15 b=20, and then work my way down?
– Carl
Nov 24 at 17:01
You could do that. But I intended to leave them as is. So for instance the first empty rectangle must contain $a+b+10-7$ to ensure the 3x3 sub grid has the same sum.
– I like Serena
Nov 24 at 17:14
Yeah okay now I see. But what should I then put inside the square next to the rectangle. Just an 8 as the square above it?
– Carl
Nov 24 at 17:27
If we shift the top left square a row down, we lose $10+a+b$, and gain $7$ plus an unknown sum. Therefore that unknown sum must be $a+b+3$. If we shift the square with $a+b,8$ a row down, we lose $a+b+8$, and gain $a+b+3$ plus the unknown square. Therefore the unknown square must be $5$.
– I like Serena
Nov 24 at 18:33
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
Hint: fill in the sums in the boxes such that every 3x3 sub grid has the same sum.
begin{array}{|ccccc|}
hline
10 & boxed{a+b} & 8 & boxed{c+d} & 11 \
\
\
7 & boxed{phantom{0quad 0}} & boxed{phantom 0} & boxed{phantom{0quad 0}} & boxed{phantom 0} \
\
\
6 & boxed{phantom{0quad 0}} & boxed{phantom 0} & boxed{phantom{0quad 0}} & boxed{phantom 0} \
hline
end{array}
answered Nov 24 at 13:58
I like Serena
3,4871718
Hint: fill in the sums in the boxes such that every 3x3 sub grid has the same sum.
begin{array}{|ccccc|}
hline
10 & boxed{a+b} & 8 & boxed{c+d} & 11 \
\
\
7 & boxed{phantom{0quad 0}} & boxed{phantom 0} & boxed{phantom{0quad 0}} & boxed{phantom 0} \
\
\
6 & boxed{phantom{0quad 0}} & boxed{phantom 0} & boxed{phantom{0quad 0}} & boxed{phantom 0} \
hline
end{array}
answered Nov 24 at 13:58
I like Serena
3,4871718
answered Nov 24 at 13:58
I like Serena
3,4871718
answered Nov 24 at 13:58
I like Serena
3,4871718
answered Nov 24 at 13:58
I like Serena
3,4871718
3,4871718
How would I know sum to start with? Should I for instance say a= 15 b=20, and then work my way down?
– Carl
Nov 24 at 17:01
You could do that. But I intended to leave them as is. So for instance the first empty rectangle must contain $a+b+10-7$ to ensure the 3x3 sub grid has the same sum.
– I like Serena
Nov 24 at 17:14
Yeah okay now I see. But what should I then put inside the square next to the rectangle. Just an 8 as the square above it?
– Carl
Nov 24 at 17:27
If we shift the top left square a row down, we lose $10+a+b$, and gain $7$ plus an unknown sum. Therefore that unknown sum must be $a+b+3$. If we shift the square with $a+b,8$ a row down, we lose $a+b+8$, and gain $a+b+3$ plus the unknown square. Therefore the unknown square must be $5$.
– I like Serena
Nov 24 at 18:33
add a comment |
How would I know sum to start with? Should I for instance say a= 15 b=20, and then work my way down?
– Carl
Nov 24 at 17:01
You could do that. But I intended to leave them as is. So for instance the first empty rectangle must contain $a+b+10-7$ to ensure the 3x3 sub grid has the same sum.
– I like Serena
Nov 24 at 17:14
Yeah okay now I see. But what should I then put inside the square next to the rectangle. Just an 8 as the square above it?
– Carl
Nov 24 at 17:27
If we shift the top left square a row down, we lose $10+a+b$, and gain $7$ plus an unknown sum. Therefore that unknown sum must be $a+b+3$. If we shift the square with $a+b,8$ a row down, we lose $a+b+8$, and gain $a+b+3$ plus the unknown square. Therefore the unknown square must be $5$.
– I like Serena
Nov 24 at 18:33
How would I know sum to start with? Should I for instance say a= 15 b=20, and then work my way down?
– Carl
Nov 24 at 17:01
How would I know sum to start with? Should I for instance say a= 15 b=20, and then work my way down?
– Carl
Nov 24 at 17:01
You could do that. But I intended to leave them as is. So for instance the first empty rectangle must contain $a+b+10-7$ to ensure the 3x3 sub grid has the same sum.
– I like Serena
Nov 24 at 17:14
You could do that. But I intended to leave them as is. So for instance the first empty rectangle must contain $a+b+10-7$ to ensure the 3x3 sub grid has the same sum.
– I like Serena
Nov 24 at 17:14
Yeah okay now I see. But what should I then put inside the square next to the rectangle. Just an 8 as the square above it?
– Carl
Nov 24 at 17:27
Yeah okay now I see. But what should I then put inside the square next to the rectangle. Just an 8 as the square above it?
– Carl
Nov 24 at 17:27
If we shift the top left square a row down, we lose $10+a+b$, and gain $7$ plus an unknown sum. Therefore that unknown sum must be $a+b+3$. If we shift the square with $a+b,8$ a row down, we lose $a+b+8$, and gain $a+b+3$ plus the unknown square. Therefore the unknown square must be $5$.
– I like Serena
Nov 24 at 18:33
If we shift the top left square a row down, we lose $10+a+b$, and gain $7$ plus an unknown sum. Therefore that unknown sum must be $a+b+3$. If we shift the square with $a+b,8$ a row down, we lose $a+b+8$, and gain $a+b+3$ plus the unknown square. Therefore the unknown square must be $5$.
– I like Serena
Nov 24 at 18:33
add a comment |
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1
Hint: Fill in as many zeroes as you can, until you are forced to put a number to make the total sum of the grid $2019$.
– Toby Mak
Nov 24 at 10:06
Also, are you sure the number in the top right corner is correct?
– Toby Mak
Nov 24 at 10:12
Cool, I will try using that strategy. That picture came with the problem, so I must assume it is correct.
– Carl
Nov 24 at 10:16