ABACUS International Math Challenge
for
3rd and 4th graders
January, 1999
A.97. A fourth grade class has 35 students
out of which 25 are girls, and 12 students wear glasses. In this class there
are 7 boys with no glasses. How many girls wear glasses in this class?
A.98. Cut up a square into
a) 6
b) 7
c) 8
smaller squares.
A.99. The following diagram shows a bus
ticket. When you get on the bus, a machine punches 4 holes on your ticket
over the numbers. A different machine punches 5 holes over the numbers.
Which machine can be programed in more different ways?
A.100. Pick three digits so that, with
their different orders, you could make three such 3-digit numbers, that
the sum of two of them is equal to the third one.
A.101. The sum of two whole numbers is
968. One of them ends with a zero, but if you delete this zero, you get
the other number. What are these numbers?
A.102. Find the smallest positive 4-digit
number in which the product of the digits is 100. Find the smallest positive
whole number in which the sum of the digits is 100.
A.103. "Look, Peter, there are red
and blue balls in these 8 boxes."- said Kate to her brother. "Both
colors may be in each box. There are 7, 10, 13, 18, 28, 31, 46, and 62 balls
in the boxes respectively. I know which box has how many red and how many
blue balls, but you do not. Now, here is your assignment: Take away one
box, so that all together there are twice as many red balls than blue balls
in the remaining 7 boxes. It is possible to do this by taking away one box."
Peter thought about this for a while, then his eyes started to shine,
and he took a box away.
Which box did he take and why?
A.104. A father left $1600 to his three
sons. In his will he said that his oldest son should get $200 more than
the middle-son, and the middle-son should get $100 more than the youngest
son. Find out how much each son should get.
by Euler (1707-1783)
Please, send your solutions to: