ABACUS International Math Challenge
for
3rd and 4th graders
March, 2004
Please, send your solutions
in by May 15, 2004.
A.425. Two Munchkins, Smidgen and Midgen,
were picking mushrooms in the forest. Smidgen picked 53 more mushrooms than
Midgen. On the way home Smidgen gave 28 mushrooms to Midgen. Now who has
more mushrooms and how much more?
A.426. 5 people wish to form pairs and
play a card game called Bridge. How many games are needed so that all possible
teams play each other?
by Jack Dillon
A.427. The Munchkin girls, Tiny and Miny,
are sewing hats. They put the finished hats, which are either red, blue,
green, or yellow, in the same color boxes as the hats. Every box has already
at least three hats, the red box has even more than 10 hats, but none of
the boxes has more than 20 hats. How many hats could the two girls possible
make already?
A.428. The Mayor of Munchkin City is putting
new tiles on his 4 tile by 4 tile sized balcony. He wants to use 4 green
and 12 yellow tiles so that every row, every column and every diagonal has
only one green tile in it. How many different ways can he do this?
A.429. In Munchkin Land they picked this
week's winning numbers on the 5-number lottery. (They picked 5 numbers out
of the numbers from 1 to 90.) The sum of any two of these 5 numbers is an
even number.
a) At least how many odd numbers can there be among the 5 winning numbers?
b) How many odd numbers can there be among the 5 winning numbers at
most?
c) At least how many even numbers can there be among the 5 winning numbers?
d) How many even numbers can there be among the 5 winning numbers at
most?
A.430. On Sunday morning the chief Gardener
of Munchkin City planted a beautiful plant in front of the City Hall. Every
day, starting this Sunday already, at noon the plant brings 5 new flowers.
A few days later somebody counted 145 flowers on the plant. What day of
the week could it be?
A.431. On a vacation 7 times rained either
before noon or after noon. If it rained before noon, then it did not rain
after noon. 5 times it did not rain before noon, and 6 times it did not
rain after noon. How many days was this vacation?
A.432. On Minny Miny's birthday party the
garden is decorated with red, green, yellow and blue helium balloons. There
is a different number of each color balloon. There are a total of 5 red
and blue. There are a total of 8 blue and green. There is the least number
of blue balloons, and the yellow balloons have the highest number of them.
There are a total of 19 balloons in the garden. How many balloons are there
from each color?
Please, send your solutions to: