MathDB

Suppose that we have a

2\times5

grid, and we wish to write

0

's and

1

's inside such that for any

2\times2

sub-block, the

<span class='latex-italic'>determinant</span>

0

. The determinant of a

2\times2

block

\textstyle\begin{bmatrix}a&b\\c&d\end{bmatrix}

ad-bc

. For example, the following is a valid configuration: However, the following is not valid because the last

2\times2

sub-block has determinant

1

: How many such valid

2\times5

configurations are there?

21