Discussion
What is the maximum number of 3 × 3 squares that can be formed from the squares in the 6 × 6 checker board to the right?
*This question is included in Nova Math - Problem Set K: Elimination Strategies, question #1
| (A) | 4 |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
Posted: 03/15/2012 19:52
Ok so the correct answer can be derived from just counting...but it's a waste of time, you can just think logically. Every 3x3 square takes up 2 spaces around its center or [3-1] and since in each of 2 directions direction there are 6 unit blocks, you'd do:
[6-(3-1)]^2 which is equal to 4^2 or 16.
Likewise, if it was a 4x4 box you'd do:
[6-(4-1)]^2 which is 9, count and check if you'd like.
Furthermore, if it were three-dimensional boxes (3x3x3 and 6x6x6)in space you,d do:
[6-(3-1)]^3 which is 64.
Basically my point is that people ought to know how to find the answers to these kinds of logistical problems, and not just how to hope to get them right on a test they are waiting to forget about.
[6-(3-1)]^2 which is equal to 4^2 or 16.
Likewise, if it was a 4x4 box you'd do:
[6-(4-1)]^2 which is 9, count and check if you'd like.
Furthermore, if it were three-dimensional boxes (3x3x3 and 6x6x6)in space you,d do:
[6-(3-1)]^3 which is 64.
Basically my point is that people ought to know how to find the answers to these kinds of logistical problems, and not just how to hope to get them right on a test they are waiting to forget about.