2024 AMC 8 Problems/Problem 17: Difference between revisions
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Multiply by two to account for arrangements of colors to get <math>\fbox{E) 32}</math> ~ c_double_sharp | Multiply by two to account for arrangements of colors to get <math>\fbox{E) 32}</math> ~ c_double_sharp | ||
==Video Solution 1 by Math-X (First understand the problem!!!)== | ==Video Solution 1 (super clear!) by Power Solve== | ||
https://youtu.be/SG4PRARL0TY | |||
==Video Solution 2 by Math-X (First understand the problem!!!)== | |||
https://youtu.be/nKTOYne7E6Y | https://youtu.be/nKTOYne7E6Y | ||
~Math-X | ~Math-X | ||
==Video Solution 3 by OmegaLearn.org== | ==Video Solution 3 by OmegaLearn.org== | ||
Revision as of 18:55, 26 January 2024
Problem
A chess king is said to attack all the squares one step away from it, horizontally, vertically, or diagonally. For instance, a king on the center square of a 
x grid attacks all 
other squares, as shown below. Suppose a white king and a black king are placed on different squares of a x grid so that they do not attack each other. In how many ways can this be done?
(A) 
(B) 
(C) 
(D) 
(E) 
Solution 1
Corners have 
spots to go and 
corners so 
.
Sides have spots to go and sides so 
in total.
is the answer.
~andliu766
Solution 2
We see that the center is not a viable spot for either of the kings to be in, as it would attack all nearby squares.
This gives three combinations:
Corner-corner: There are 4 corners, and none of them are touching orthogonally or diagonally, so it's 
Corner-edge: For each corner, there are two edges that don't border it, 
Edge-edge: The only possible combinations of this that work are top-bottom and left-right edges, so 
for this type
Multiply by two to account for arrangements of colors to get 
~ c_double_sharp
Video Solution 1 (super clear!) by Power Solve
Video Solution 2 by Math-X (First understand the problem!!!)
~Math-X
