ABACUS International Math Challenge
for
3rd and 4th graders
February, 1999
A.105. Can you distribute
100 rabbits between 5 children so that every child would get an odd number
of rabbits?
A.106. Four cards are laying on the table
in front of you. We know that every card has a letter on one side and a
number on the other side. You see the following signs on the top sides of
the 4 cards:
Your assignments is to decide whether the following statement is true
or false: "If a card has a vowel on one side, then it has an even number
on its other side."
At least how many cards do you have to turn over in order to be able
to decide?
A.107. A bug is climbing up on the trunk
of a tree. During the day it climbs up 4 meters, but at night it slides
back down 3 meters. On the ninth day it reaches the top of the tree. How
tall is the tree?
A.108. Write the numbers 1, 2, 3, ...,
9 in a 3x3 grid so that the sums of the three numbers in the columns, rows,
and diagonals are all different.
A.109. Three travelers arrive to a hotel.
They order a bowl of meatballs. By the time the chef makes their dinner,
they fall asleep. at the table. Later one of the travelers wakes up and
eats a third of the meatballs, them falls back to sleep. A little while
later another traveler wakes up and eats the third of the remaining meatballs,
then falls back to sleep. Finally the third traveler wakes up and eats the
third of the remaining meatballs, and now there are 8 meatballs left in
the bowl. How many meatballs did the chef prepare for the travelers?
A.110. In my family nobody is married to
a blood-relative. Is it true that the grandfathers of my great grandfathers
are the same people as the great grandfathers of my grandfathers?
A.111. In a box there are four kinds of
colored balls, a total of 40 of them. We know that blind-folded you have
to take out at least 32 of them in order to have at least one of each of
the four kinds of balls.
a) At least how many balls are there from each of the colors in the
box?
b) At most how many balls can you have from each of the colors?
A.112. In a warehouse there are two identical
barrels: one of them is full of oil, the other one is exactly half way.
Their masses are 86 kg and 53 kg. What is the mass of an empty barrel?
Please, send your solutions to: