## Task 2 - 340532

From exactly 4 sticks, each of which is slightly less than $1 \mathrm{~cm}$ in length, a small square with a side length of $1 \mathrm{~cm}$ can be formed:

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0148.jpg?height=66&width=88&top_left_y=1646&top_left_x=984)

For a square consisting of four of the previously considered small squares, exactly 12 sticks are required:

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0148.jpg?height=123&width=120&top_left_y=1840&top_left_x=974)

(a) How many sticks exactly are needed for a square that consists of (1) nine, (2) sixteen of these small squares?

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0148.jpg?height=223&width=219&top_left_y=2090&top_left_x=927)

How many sticks exactly are needed to lay out a square grid that is $1 \mathrm{~m}$ long and $1 \mathrm{~m}$ wide using these small squares?

No justification is required.
(a) One needs

(1) exactly $(3 \cdot 4+3 \cdot 4=) 24$ sticks,

(2) exactly $(4 \cdot 5+4 \cdot 5=) 40$ sticks.
(b) For this square grid of 100 $\cdot$ 100 small squares, one needs (in each horizontal row 101 vertical sticks, in all horizontal rows together thus 100 - 101 vertical sticks; equally many horizontal sticks in all vertical rows; in total thus) exactly (100 $101+100$ $\cdot$ $101=) 20200$ sticks.