1. The fourth grade of the School for Wizards has 20 students. All students participated in the construction of a tower. Ten students were stacking blocks one on top of the other so that each placed twice as many blocks as the previous one. The first student placed one block, the second two blocks, the third four blocks, and so on. After that, the remaining students took blocks from the top, with the first taking one block, the second taking two, the third taking three, and so on, up to the last remaining student. What is the final height of the constructed tower if the height of each block is $5 \mathrm{~cm}$?
1. The fourth grade of the School for Wizards has 20 students. All students participated in the construction of a tower. Ten students were stacking blocks one on top of the other so that each placed twice as many blocks as the previous one. The first student placed one block, the second two blocks, the third four blocks, and so on. After that, the remaining students took blocks from the top, with the first taking one block, the second two blocks, the third three blocks, and so on until the last remaining student. What is the final height of the constructed tower if the height of each block is $5 \mathrm{~cm}$?

## Solution.

$1+2+4+8+16+32+64+128+256+512 \quad 2$ POINTS

$=1023 \quad 1$ POINT

Ten students built a tower of 1023 blocks.

$10$ students took blocks from the tower.

$20-10=10$ students.

$1$ POINT

$1+2+3+4+5+6+7+8+9+10 \quad 2$ POINTS

$=55$

1 POINT

They took 55 blocks.

$1023-55=968$ blocks remained.

$1$ POINT

The height of the tower is $968 \cdot 5=4840 \mathrm{~cm}$.

2 POINTS

TOTAL 10 POINTS