ABACUS International Math Challenge
for
5th and 6th graders
January, 2004
B.409. The 2-headed and the 7-headed dragons
held a meeting. The king of the 7-headed dragons made a head-count at the
beginning of the meeting. He looked around with his crowned middle head
and saw 25 heads, so he acknowledged that everybody was present. How many
2-headed and how many 7-headed dragons were present?
B.410. Three teams made it to the finals
of the volleyball championship. Every team played twice with every team,
once at home and once on the opponent's home court. (In volleyball there
is no tie, one of the two teams always wins.) The Eagles never beat the
Hyenas, and even though the Rockets lost two games, they never lost at home.
Who won the Championship, and who finished on second and third place?
B.411. What fraction of the area of the
rectangle is the shaded area?
B.412. Three people: Fred, who always tells
the truth; Ben, who sometimes tells the truth but other times she lies;
and Bonehead, who never tells the truth, run one behind another in the park.
We do not know who is running first, second and third, but they each said
the following word:
The first person running in the front: "Fred is running in the
middle."
The second person: "I am Ben."
The third person: "Bonehead is running in the front."
Who is running first, second and third?
B.413. The family has a garden party for
Grandma's birthday where all of Grandma's grandchildren are present. Out
of the grandchildren, John has his 3 cousins, Julie has 4 cousins, and Dori
has 5 cousins present. How many grandchildren does Grandma have?
B.414. Lulu loves to play with dice. Therefore,
his friends surprised him on his birthday with an interesting present: they
used 22 not necessarily identical, but regular dice (the sum of the dots
on the opposite sides always add up to 7), they glued some of them together
so that they would form the letters of his name and show one dot on each
front side, as shown on the diagram. Finally they painted each letter completely
blue on the outside. What is the most dots that the none-painted sides of
the cubes could possible have on them all together?
B.415. Tom spent the first one third of
his life in the USA, then he spent 1/6 of his life in India. After that
he lived in Egypt for 12 years, and then for the half of the rest of his
life he lived in Australia. Then he moved to Canada and lived there until
his death as long as he lived in India. Where did he celebrate his 40th
birthday?
B.416. On planet Urp one year is 18 months
long, and every month has 10 days. Every 7th year is a leap year (one day
longer than the other years) when the 3rd month has 11 days. Every week
has 5 days: Moonday, Twosday, Restday, Fryday, Schoolday. Dourp, one of
the people from Urp, was born on Fryday, on the first day of the 4th months
of a leap year. What day of the week did he celebrate his 15th birthday?
Please, send your solutions to: