ABACUS International Math Competition
for
3rd and 4th graders
April, 1998
A.57. Andrew, his younger twin-brothers,
and their father have the same birthday. On their birthday in 1998 the product
of their ages is 1998. What could the sum of their ages be?
by Bognár Ferencné, Hungary
A.58. In this addition same letters mean
same digits, different letters mean different digits. What number is 
?
A.59. Write every whole number from 1 to
9 in a 3x3 grid so that the sum of the two 3-digit numbers created from
the first and the second rows is equal to the 3-digit number created from
the third row, and similarly, the sum of the two 3-digit numbers created
from the first and the second columns is equal to the 3-digit number created
from the third column. (In the columns you read from top to bottom.)
A.60. 10 new suitcases and an envelope
with the keys to them in it arrived to a bag shop. Every key opens only
one suitcase. At least how many tries is necessary to find the right key
to every suitcase?
A.61. In a class 14 students collect stamps,
16 students collect postcards. 5 students collect both, but 4 students collect
neither. How many students are there in the class?
A.62. Write different positive whole numbers
in the rectangles so that every one of them is the sum of the two numbers
below it, and the number in the top rectangle is the smallest possible.
A.63. Break up the number 45 into 4 parts
so that if you add 2 to the first part, subtract 2 from the second part,
multiply the third part by 2, and divide the fourth part by 2 you get equal
numbers.
A.64. The sum of four numbers is 1998.
Could the last digit of their product be 1?
Please, send your solutions to:
Solutions of last year's problems