ABACUS International Math Challenge
for
3rd and 4th graders
January, 2008
A.617. In the last half an hour of an evening
TV program there will be a poem recital, a ballet performance, a folk dance
performance, and a story-teller. In how many different orders can the director
put these performers if the two dance performances cannot follow one another?
A.618. There are 4 boys and 5 girls in
the Polka dots folk dance company. After two and a half minutes of group
dance every boy dances a half-minute pair-dance with every girl. How long
is the company's performance?
A.619. There are 156 seats in the school's
theater. On the first performance of the latest musical a thirds of the
seats were taken, on the second performance a quarter of the seats were
empty, on the third performance only 28 seats were empty. On the final performance
there were so many people that a third of them had to be standing because
all the seats were taken. How many tickets were sold for the 4 performances
if ever spectator bought a ticket?
A.620. On the school's talent show each
of the four judges used a 1 - 10 scale to evaluate the performances. For
her singing, Melissa received a different score from every judge. If you
add any two of these scores, you get the following sums: 11, 12, 14, 15,
17, and 18. What is the total number of points Melissa received from the
judges?
A.621. There are four instruments in a
string quartet: violin, viola, cello, and bass. In the piece they played
not all four instruments were used all the time. Sometimes only one, two
or three instruments played at the same time, but of course, many times
all four of them made music together. In how many different arrangements
could we hear the instruments playing?
A.622. In a fourth grade class many of
the 23 students participated in the Talent Show. 10 of them danced, 9 of
them sang, 7 of them played an instrument. 3 students danced and played
an instrument, also. 5 students played an instrument and sang, as well.
6 students sang and danced, also. Only 2 students showed all three of these
talents. How many students showed only one of their talents? How many students
did not participate in the Talent Show from this class?
A.623. In a pet store there is a huge,
3-story bird cage. 21 birds live above, and 24 birds live below other birds
in this cage. Just as many birds live on the middle level than on the bottom
and on the top together. How many birds live on each level?
A.624. Two painted turtles (Ann and Bella)
are 5 meters apart. They start crawling towards each other at the same time.
Ann can crawl 70 cm in 2 minutes, and Bella can crawl 20 cm in one minute.
How far will they be from each other 8 minutes later?
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