p1. A conical bottle perched on its base is filled with water up to a height that is $ 8$ cm of its vertex. When the bottle is turned over the water level is at $2$ cm from its base. Calculate the height of the bottle. p2. A square with side $ 8$ cm is divided into $64$ squares of $ 1$ cm$^2$. $7$ little squares are colored black and the rest white. Find the maximum area of a rectangle composed only of small white squares independent of the distribution of the little black squares. p3. From a $1000$-page book, a quantity has been ripped of consecutive of leaves. It is known that the sum of the numbers of the torn pages is $2018$. Determine the numbering of the ripped pages. p4. Given a rhombus $ABCD$, a circle with center at the midpoint of side $AB$ and with diameter $AB$ is drawn, which intersects side $BC$ at the point $K$. Similarly, a circle is drawn with its center at the midpoint of side $AD$ and of diameter $AD$ that cuts to the side $CD$ at point $L$. Suppose that $\angle AKL = \angle ABC$. Determine the angles of the rhombus sides are equal. PS. Juniors p2, p3 were posted as Seniors p2,p1 respectively.