So a picture appeared on FB asking for the answer to the picture below, to which many people
responded "14".
Everywhere I looked, people answered 14. However, I stood out because I was the only one who said that the answer is 11.25.
The problem can be represented algebraically like this:
4x = 5
x = 1.25
9x = ?
9(1.25) = 11.25
So my question is..how the heck did people get 14? Am I using the wrong approach?
Best Answer
The first picture shows $5$ squares, the $4$ smaller ones, along with the $2\times 2$ square. Counting $1\times 1$, $2\times 2$, and $3\times 3$ squares, the second picture shows $14$ squares.
With this reasoning, a $4\times 4$ grid would equal $30$.
In general, an $n\times n$ grid would equal $1^2+2^2+\ldots+n^2=\frac{n(n+1)(2n+1)}{6}$.
These are the square pyramidal numbers, because they are the number of cubes needed to build a pyramid with a square base $n$ levels high.