ABACUS International Math Challenge
for
5th and 6th graders
February, 2007
(These is the last set of questions
for this year!
Please, send all your solutions in by April
30, 2007.)
B.577. Place all the positive whole numbers
from 1 to 10 into the circles of the following diagram so that the number
in each circle is the difference of the two numbers right above it.
B.578. Four married couples went to four
different places on Saturday night to have some fun and relax. Everybody
was with his or her own spouse. The husbands are: Andrew, Ben, Cole, and
Daniel; the wives are Emma, Fanny, Gizelle, and Helga. Andrew went to a
concert. Ben spent the evening with Emma, but Cole did not see Gizelle that
night. Fanny saw a movie, Gizelle went to the theater. One of the couples
was at a wedding. Who are spouses of each other, and where did they all
go that night?
B.579. A positive whole number is 20 more
when rounded to the nearest 100 than when rounded to the nearest 10. Add
all of these numbers below 1000. What is the sum?
B.580. My friend has three clocks in his
apartment: an analog mechanical clock that always shows the correct time,
and one analog and one digital electric clocks, which are operated by the
wall outlet in his apartment. If there is a blackout (no electricity in
the apartment) the analog electric clock stops but when the electric service
is restores this clock continues from the time it showed when it was stopped.
However, the digital electric clock zeros its screen at a blackout, and
when the electric service is back, this clock, while blinking, starts measuring
time again from midnight. My friend went to work one morning when all of
his clocks showed 6:30. On his return that evening he saw that his mechanical
clock shows 8:21, the analog electric clock shows 7:50, and the digital
electric clock shows 6:03 while blinking. Suppose that there was only one
blackout period, from what time to what time did it happen?
B.581. Five teams compete in a sports competition:
A, B, C, D, and E. Two people take a guess on the final order of the teams.
These are (starting with the first place team and going down) ABCDE and
BDEAC. The first guesser got the correct final place of exactly three teams,
the second guesser got the correct final place of exactly two teams. What
was the actual final standing?
B.582. Break up 60 into the sum of two
numbers so that one seventh of one of the numbers is the same as one eighth
of the other number.
B.583. Tom wrote a novel on his computer
with continuing page numbers on it. The first page had page number one on
it. He printed his book on his printer (double sided sheets) and took it
to a book binder, but he was told there that this way the book would be
too thick. So, instead, they put the novel into three books (volumes) with
the same number of pages in them. (They kept the original page numbers on
each page.) If you add the page numbers on the first page of each of the
three books, you get 1353. How many pages long is the novel?
B.584. I have only $10 and $20 bills in
my pocket. There are three times as many $20 bills than $10 bills. I have
a total of $490. How many $20 bills do I have?