helpinghumanity
Junior Member
:salam2:
PROBLEM 1:
Is it possible to attach together tiles with the following shape to cover the
whole plane without holes or any overlap of tiles? (Each tile consists of 5
identical squares.)
Please Open the attached file to view the picture
PROBLEM 2:
The World Series is a best-of-seven contest. (Two baseball teams play up to 7 games against each other. As soon
as 1 team has won 4 games, the contest is over.) If teams A and B play in the series, a sequence of winners for the
games played might be AAAA or ABBABAB, but not AAAAB. How many different sequences of winners for the
games of a World Series between Team A and Team B are possible?
PROBLEM 3:
Evaluate the expression shown below given that the first number under the square root sign has 2008 digits (all of
which are ones) and the second number has 1004 digits (all of which are twos).
(111…111) - (222…222)
PROBLEM 4:
How many different rectangles which are not squares can be found on a chess board? (A chess board has 8 rows
and 8 columns of squares. A rectangle on the board is a collection of squares that form a rectangular piece of the
whole board. Two rectangles are different if they have different sets of squares. A rectangle with an unequal number
of rows and columns is not square.)
PROBLEM 5
A spherical ball with radius 1 is covered with ink and is placed in the hollow region between two concentric spheres
with radii 3 and 5. The inked ball rolls about in this region, always touching the inside surface of the outer sphere and
the outside surface of the inner sphere. Suppose that a region with area 1 on the outer sphere gets painted with ink
by the rolling ball. Find the area of the region of the inner sphere that gets inked by the rolling ball.
PROBLEM 1:
Is it possible to attach together tiles with the following shape to cover the
whole plane without holes or any overlap of tiles? (Each tile consists of 5
identical squares.)
Please Open the attached file to view the picture
PROBLEM 2:
The World Series is a best-of-seven contest. (Two baseball teams play up to 7 games against each other. As soon
as 1 team has won 4 games, the contest is over.) If teams A and B play in the series, a sequence of winners for the
games played might be AAAA or ABBABAB, but not AAAAB. How many different sequences of winners for the
games of a World Series between Team A and Team B are possible?
PROBLEM 3:
Evaluate the expression shown below given that the first number under the square root sign has 2008 digits (all of
which are ones) and the second number has 1004 digits (all of which are twos).
(111…111) - (222…222)
PROBLEM 4:
How many different rectangles which are not squares can be found on a chess board? (A chess board has 8 rows
and 8 columns of squares. A rectangle on the board is a collection of squares that form a rectangular piece of the
whole board. Two rectangles are different if they have different sets of squares. A rectangle with an unequal number
of rows and columns is not square.)
PROBLEM 5
A spherical ball with radius 1 is covered with ink and is placed in the hollow region between two concentric spheres
with radii 3 and 5. The inked ball rolls about in this region, always touching the inside surface of the outer sphere and
the outside surface of the inner sphere. Suppose that a region with area 1 on the outer sphere gets painted with ink
by the rolling ball. Find the area of the region of the inner sphere that gets inked by the rolling ball.
but am gonna give a shot on this in my spare time in sha allah.