ABACUS International Math Challenge
for
7th and 8th graders
September, 2005
C.489. The 5 squares on the diagram below
are made of match sticks. (Every side is a stick.) Relocate (move to a different
location) two match sticks on the table, so there are only 4 squares of
the same size as the original squares.
C.490. In the following product (AxBxAxCxUxS)
x (IxLxOxVxExIxT) different letters mean different digits, the same letters
mean the same digits. What is the ratio of the greatest and the smallest
possible values of this product?
C.491. To put a figure on each of the fields
on the edges and each field of one of the diagonals of a square-shaped chess-like
board we used 404 figures. How many empty fields are still there on this
board?
C.492. We wrote down all the 3-digit numbers
in an increasing order, so that we used a red pen for the even numbers'
digits and a blue pen for the odd numbers' digits. How many red 8's are
there on the paper?
C.493. On a square grid paper we drew a
spiral line along the grids. The diagram shows the rules of creating the
spiral line. The shortest (first) segment is 1 cm long.
a) How long is the spiral line if the last two segments are both 40
cm long?
b) If you checked the length of the spiral line at every turn you make,
can you ever find it to be 1500 cm long?
C.494. The 5 squares on the diagram below
are made of match sticks. (Every side is a stick.) Can you relocate (move
to a different location) two match sticks on the table, so there are only
4 squares of the same size as the original squares?
C.495. I am standing in a single line at
the post office. (People are standing one-by-one, one person behind another.)
There are two more people in front of me than behind me, and there are 3
times as many people in the whole line than behind me. How many people are
in the line and where in the line am I standing?
C.496. A kind of pen was sold for 50 cents,
but very few people bought it. Therefore, they reduced its price by less
then 50%. (Its new price is whole cents, also.) This way they sold the whole
inventory. Since they reduced the price of the pen, they collected $31.93.
What was the reduced price of the pen?