ABACUS International Math Competition
for
5th and 6th graders
February, 1998
B.41. The lengths of the sides of a triangle
are the a, b, c whole numbers, and b+c=5a. Out of these kind of triangles,
find the one with the smallest perimeter.
B.42. In the history of France between
1700 and 1900 two important victories were noted on the days of April 22.
Based on the following two information, find the years of these victories:
a) The second victory happened 4382 days later than the first one.
b) The sum of the digits of the year of the first victory is 23.
B.43. How many 4-digit-numbers are there
in which the digits 1 and 2 are both represented?
B.44. Using the digits 0, 0, 1, 1, 2, 2,
3, 3, find numbers in which there is 0 digits between the two zeros, there
is 1 digit between the two 1's, there are two digits between the two 2's,
and there are three digits between the two 3's.
B.45. In the following multiplication same
letters mean same digits, different letters mean different digits. What
number is the word
?
B.46. Using all the non-zero digits exactly
once, write down 3 numbers with a ratio of 1:2:3.
B.47. Can you write numbers in the fields
of a 5x5 grid so that in any 2x2 part of the grid the sum of the four numbers
should be negative, while in any 3x3 part of the grid the sum of the nine
numbers is positive.
B.48. A class has 33 students. Each day,
22 of them swim and 22 of them play soccer. Every day everybody takes part
in at least one of these two sports. Out of those who play soccer today,
15 went to swim yesterday and 15 played soccer yesterday. The same is true
of those 22 students who swim today. How many students went only to swim
on both days?
Please, send your solutions to:
Solutions of previous problems