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MATH / Below is a magic square, meaning that the sum of the numbers in each row, in…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Below is a magic square, meaning that the sum of the numbers in each row, in each column, and in each of the 22 main diagonals are equal. What is the value of nn? [asy]size(125); for(int i = 0; i<4; ++i) { draw((0,i)--(3,i),linewidth(1)); } for(int j = 0; j<4; ++j) { draw((j,0)--(j,3),linewidth(1)); } label("n−3n-3",(.5,.5)); label("3",(.5,1.5)); label("n+1n+1",(.5,2.5)); label("n+2n+2",(1.5,.5)); label("2n−92n-9",(1.5,1.5)); label("11",(1.5,2.5)); label("22",(2.5,.5)); label("nn",(2.5,1.5)); label("n−1n-1",(2.5,2.5)); [/asy]
Plain-text mathematical notation (without MathML)
Below is a magic square, meaning that the sum of the numbers in each row, in each column, and in each of the 2 main diagonals are equal. What is the value of n?

[asy]size(125);
for(int i = 0; i<4; ++i)
{

draw((0,i)--(3,i),linewidth(1));
}

for(int j = 0; j<4; ++j)
{

draw((j,0)--(j,3),linewidth(1));
}

label("n−3",(.5,.5));
label("3",(.5,1.5));
label("n+1",(.5,2.5));

label("n+2",(1.5,.5));
label("2n−9",(1.5,1.5));
label("1",(1.5,2.5));

label("2",(2.5,.5));
label("n",(2.5,1.5));
label("n−1",(2.5,2.5));
[/asy]
Original LaTeX notation
Below is a magic square, meaning that the sum of the numbers in each row, in each column, and in each of the $2$ main diagonals are equal. What is the value of $n$?

[asy]size(125);
for(int i = 0; i<4; ++i)
{

draw((0,i)--(3,i),linewidth(1));
}

for(int j = 0; j<4; ++j)
{

draw((j,0)--(j,3),linewidth(1));
}

label("$n-3$",(.5,.5));
label("3",(.5,1.5));
label("$n+1$",(.5,2.5));

label("$n+2$",(1.5,.5));
label("$2n-9$",(1.5,1.5));
label("$1$",(1.5,2.5));

label("$2$",(2.5,.5));
label("$n$",(2.5,1.5));
label("$n-1$",(2.5,2.5));
[/asy]

level

Level 5

type

Prealgebra

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Source and history

task_id
4b81acfe-2e17-5667-91dc-48acdbb3a865
task_key
prealgebra--test--4b81acfe-2e17-5667-91dc-48acdbb3a865
task_revision_id
1
config / split
prealgebra / test

Official source

initial import