ABACUS International Math Challenge
for
5th and 6th graders
March, 1999
B.113. Add seven different fractions with numerators
1 to get 1.
B.114. Using the same digits, and using
operation signs, create 1996. Find a solution with the least number of digits
used.
B.115. Find this number: if you divide
273437 by it, you get a remainder of 17; if you divide 272758 by it, you
get a remainder of 13.
B.116. Four people made the following statements
about a quadrilateral:
Andrew: "It is a square."
Ben: "It is a parallelogram."
Cecilia: "It is a trapezoid."
Don: "It is a deltoid."
What can you say about this quadrilateral if three of these statements
are true, but one of them is false?
B.117. Write the numbers 1, 2, 3, 4, 5,
6, 7, 8, and 9 into the circles so that the sums of teh numberson every
segment are the same, and that this sum is the greatest possible.
B.118. Take a subset of the numbers1, 2,
3, ..., 99, 100, in which none of the elements is three times as big as
any other element in the subset. How many elementscan such a subset have
the most?
B.119. My watch is 5/6 of a minute, my
clock is one and a half minutes late every day. On Monday at noon I set
them to show the correct time. Within a week, I asked my mother what time
it was. She said: "I don't know, but the time difference between your
watch and your clock is 4 minutes and 15 seconds." What day and what
time did I ask my mother what time it was?
B.120. Separate the numbers 1, 2, 3, ...,
15, 16, into two groups of eight numbers, so that if you calculate the sums
of any two (different) numbers in one group, then you get the same answers
(and every one of them the same number of times) as if you did the same
with the numbers in the other group.
Please, send your solutions to: