16. Assemble a square using four $1 \times 1$ square tiles, eight $2 \times 2$ square tiles, twelve $3 \times 3$ square tiles, and sixteen $4 \times 4$ square tiles.
16. The area of all the tiles, and thus of the desired square, is $1 \cdot 4 + 4 \cdot 8 + 9 \cdot 12 + 16 \cdot 16 = 400$ (sq. units). Therefore, we need to form a square with a side length of 20 units. The available tiles can be arranged as shown in Fig. 24.

![](https://cdn.mathpix.com/cropped/2024_05_21_00604dc020e3721fc1f4g-178.jpg?height=460&width=620&top_left_y=1575&top_left_x=341)

Fig. 20

![](https://cdn.mathpix.com/cropped/2024_05_21_00604dc020e3721fc1f4g-178.jpg?height=474&width=626&top_left_y=1576&top_left_x=1069)

Fig. 21

![](https://cdn.mathpix.com/cropped/2024_05_21_00604dc020e3721fc1f4g-179.jpg?height=474&width=648&top_left_y=226&top_left_x=356)

Fig. 22

![](https://cdn.mathpix.com/cropped/2024_05_21_00604dc020e3721fc1f4g-179.jpg?height=474&width=643&top_left_y=226&top_left_x=1095)

Fig. 23

Fig. 24

![](https://cdn.mathpix.com/cropped/2024_05_21_00604dc020e3721fc1f4g-179.jpg?height=1060&width=1037&top_left_y=852&top_left_x=544)