ABACUS International Math Challenge
for
7th and 8th graders
February, 2008
C.625. What is the least number of steps
(when you switch two neighboring numbers) in which you can change the order
of the following number sequence so that the numbers are in a decreasing
order from left to right?
9; 7; 5; 10; 8; 4; 3; 6; 1; 2
C.626. In a clothing store 40% of the merchandise
are skirts. There are half as many pants as sweaters. There are no other
kinds of items in the store. 80% of all the items are for women. The store
has the same number of pants for women as sweaters for women. What percent
of all the items are men pants? (Men do not wear skirts.)
C.627. The diagram below shows the sketch
of a train station with one main line. How many different way can a train
coming from the left go through this station?
C.628. How many different ways can you
take the shortest road from c5 to h2 with a King?
C.629. Fill up a cube with 12-cm edges
5/8 of the way with water, then tilt it around one edge. The diagram below
shows a cross section of the cube with the horizontal line representing
the water level in it. You know that LC is twice as long as KB. How long
is LC?
C.630. Olga has 5 different rings, all
of them can fit on her ring finger, as well as her middle finger. She always
wears 2 rings on her ring finger and 3 rings on her middle finger, but only
on her left hand. How many different ways can she wear these rings?
C.631. As you can see below, I drew two
squares into a 30 cm x 30 cm square. How much is the difference of et areas
of squares A and B?
C.632. Last time Uncle Tom went to the
theater, he noticed the following: even when his wife is wearing 10 cm high
heels, she is 2 cm shorter than he is; Uncle Tom himself, when wearing his
33-cm tall cylinder hat, is 1 meter taller than their daughter, Dorca. How
tall are the members of this family if the mother and daughter together
(without the high heels and the cylinder hat) are 1 meter taller than Uncle
Tom?