ABACUS International Math Challenge
for
5th and 6th graders
December, 2001
B.281. Danny and Tommy are brothers. They
both have a square-shaped room that can be tiled by using 25cmx25cm wooden
tiles without having to cut any tile. In Danny's room they had to use 27
more tiles than in Tommy's room. What did the boys' parents pay for the
tiles if a tile costs $1.24?
B.282. There are red, blue and green balls
of the same size and weight in a box, 10 of each. How many different ways
can you take 10 balls out of the box if you want to have at least one of
each kind? (You cannot tell two balls of the same color apart.)
B.283. What is 3@8 equal to, if 1@1=2,
3@5=34, 6@9=117, and 10@14=296?
B.284. There are red and white balls in
a box, 58 balls all together. If you take out 6 times as many white balls
as red, there are 5 times as many red as white balls left in the box. How
many red and how many white balls were in the box originally?
B.285. You fill in the fields of a 13x13
grid by writing either +1 or -1 in every field. Then you write the sum of
each column underneath it, and write the sum of each row at the right end
of it. This way you get 13-13 numbers on the bottom and on the right side
of the grid. Could the sum of these 26 numbers be zero?
B.286. Using three regular triangles we
made a trapezoid. Cut it up into 4 identical parts.
B.287. In a family the sum of the ages
of the father, the mother, their son and their daughter is 73. The father
is 3 years older than the mother, their daughter is 2 years older than their
son. The sum of their ages 4 years ago was 58. How old are they now?
B.288. Sue is making a necklace. She puts
pearls that are numbered by consecutive numbers on a lace starting with
1, then taking the number 2, and so on. When she is done, she ties the lace,
and puts the closed necklace on the table in an arrangement as shown on
the figure below. This way the number 19 and number 10 pearls are next to
each other, and the number 37 and number 52 pearls are next to each other,
also. How many pearls did Sue use to make this necklace?
Please, send your solutions to: