ABACUS International Math Challenge
for
7th and 8th graders
April, 2000
C.185. Cut up a 2x5 rectangle into 4 similar
pieces.
C.186. Can you cut up a square into two
congruent polygons where the number of sides the polygons have is
a) 7
b) 8?
C.187. In the following addition different
letters mean different numbers and the same letters mean the same numbers.
What number is ABCDEFD?
C.188. Rabbit made presents for all of
her costumers and Eeyore for Easter. But Rabbit's costumers made presents
for Eeyore, Rabbit and for each other, also. Then they all gathered at Winnie-the-Pooh's
house and put their presents under the tree. Winnie and Tigger counted the
presents, then Tigger told Winnie: "Hmm, the number of presents is
such a 3-digit number that is greater than 200, and every digit of it is
a square number. Tell me, my dearest bear friend, how many costumers does
Rabbit have?"
C.189. How many whole number solutions
does the |x|+|y|<1000 inequality have?
C.190. A soccer ball is a polyhedron that
has 32 faces which are either regular pentagons or regular hexagons. How
many edges does a soccer ball have?
C.191. Take all those 5-digit numbers in
which the sum of the digits is 37. Out of these numbers, how many are even
and how many are odd?
C.192. Can you divide 10000 pebbles into
100 groups so that every group has a different number of pebbles, but if
you make two groups out of any one of these 100 groups, the same thing is
not true for the 101 groups?
Please, send your solutions to: