ABACUS International Math Challenge
for
7th and 8th graders
March, 2004
Please, send your solutions
in by May 15, 2004.
C.425. The perimeter of a rhombus is 24
cm, its area is 18 sq.cm. How big are its angles?
C.426. Find the smallest 3-digit prime
number with all different but only prime digits.
C.427. On a digital clock you can see the
time from 00:00 to 23:59. In a day, what is the total amount of time while
you can see 3 identical digits on the clock?
C.428. Could the product of 13 consecutive
positive whole numbers be 645 127 398 020 820?
C.429. Find 5 square numbers using every
positive digit only once.
C.430. There are 1000 points on a plane.
We know that at least 3 out of any 4 points are on the same straight line.
Prove that all of them with the exception of one point the most are on the
same straight line.
C.431. How big are the angles of an isosceles
triangle if it has an angle bisector that divides the triangle into two
isosceles triangles?
C.432. Two kids are playing cards. There
are 32 cards in the deck, and every card has its pair. At the beginning
every player gets 5 cards, and then they take one card at a time from the
rest of the deck. When the deck is gone they take a card from each other,
alternating. If you have a pair (or two pairs), you must put it (them) on
the table in front of you. Prove that at the end of the game each player
has the same number of pairs.