ABACUS International Math Challenge
for
7th and 8th graders
December, 2000
C.217. In Lalaland there are no two citizens
who have the same exact teeth missing. What is the population of this magic
country if everybody could have maximum 32 teeth, but only the president
has a full set of teeth?
C.218. How many different tetrahedrons
are there with whole number-long edges, and with 17 as the sum of the lengths
of the edges?
C.219. Find all the 4-digit square numbers
with only even digits.
C.220. Is there such a square number where
the first 9 digits are 123456789, and the last nine digits are 987654321?
C.221. There are 3 points given on a plain
so that they are not on the same straight line. How many straight lines
are there on this plain that are equidistant from all three of these points?
C.222. Tigger left his house for a long
trip to visit Roo, the kangaroo. On the first day he made a quarter of the
trip, on the second day he made a third of the remaining distance, on the
third day he made a half of the remaining distance. How far does Roo live
from Tigger, if Tigger had to walk 27km on the fourth day to get there?
C.223. Adam offers a game to Ben: he tosses
three silver dollar coins up in the air; if all three of them are heads
or all three of them are tails then Adam pays $200 to Ben; if the coins
lend otherwise then Ben has to pay Adam $100.
What should Ben do: should he accept or should he refuse to play this
game?
C.224. Five girls and three boys are playing
volleyball. How many different ways can they make two teams of four players
so that both teams have at least one boy?
Please, send your solutions to: