2016 AMC 12B Problems/Problem 12

Problem

All the numbers $1, 2, 3, 4, 5, 6, 7, 8, 9$ are written in a $3\times3$ array of squares, one number in each square, in such a way that if two numbers of consecutive then they occupy squares that share an edge. The numbers in the four corners add up to $18$ . What is the number in the center?

$\textbf{(A)}\ 5\qquad\textbf{(B)}\ 6\qquad\textbf{(C)}\ 7\qquad\textbf{(D)}\ 8\qquad\textbf{(E)}\ 9$

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

Solution by Mlux: Draw a $3\times3$ matrix. Notice that no adjacent numbers could be in the corners since two consecutive numbers must share an edge. Now find 4 nonconsecutive numbers that add up to $18$ . Trying $1+3+5+9 = 18$ works. Place each odd number in the corner in a clockwise order. Then fill in the spaces. There has to be a $2$ in between the $1$ and $3$ . There is a $4$ between $3$ and $5$ . The final grid should similar to this.

$\newline 1, 2, 3\newline 8, 7, 4\newline 9, 6, 5$

$\textbf{(C)}7$ is in the middle.

2016 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 11	Followed by Problem 13
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 12 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

Page

Toolbox

Search

2016 AMC 12B Problems/Problem 12

Problem

Solution

See Also