ABACUS International Math Challenge
for
5th and 6th graders
September, 2001
B.257. Eink, Oink, and Uink, the three
piglets, participate in a cake-eating contest. Grandma made the following
statements before the start:
a) Eink will be second.
b) Oink will not win.
c) Uink will not be second.
The three piglets won a first, a second, and a third place in the competition,
but only one of grandma's predictions was true. Who finished on what place?
B.258. Fill in the blanks with the numbers
from 1 to 9 using all of them, so that the chain of equalities is true:
B.259. A bank card has a 14-digit number
on it. The sum of any three consecutive digits is 13. The second digit is
2, the 13th digit is 4. What is the number on this bank card?
B.260. The following options are presented
to a young worker for the first year on his new job: he gets an initial
$1500 per month salary, gets paid biweekly, and gets a $15 increase on every
paycheck starting with the second paycheck; or he gets an initial $1500
per month salary, gets paid monthly, and gets a $60 increase on every paycheck.
Which option should he choose to make more money by the end of the first
year?
B.261. In a military unit the officer with
the highest rank is a captain. Besides him, there is one first lieutenant,
2 second lieutenants, 12 sergeants, and many privates. The number of inferiors
is 10 times the number of superiors. How many people are there in this unit?
(A person is called a superior if there is another person in his unit
with a lower rank. A person is called an inferior if there is another person
in his unit with a higher rank.)
B.262. Find the K, E, D consecutive 1-digit
numbers and the G, B different from these, but still consecutive 1-digit
numbers so that KED = E x GB (where the x represents a multiplication sign).
B.263. At the end of a party everybody
shakes hands with everybody. Suddenly, the neighbor stops by, but he shakes
hands only with those he knows. There is a total of 68 hand shakes. How
many people does the neighbor know?
B.264. Mother Goose lines up her 4 goslings
to take them to a nearby lake for a swim. On the way the goslings switch
places to change the order to their likings. We know the following about
the new lineup:
1) Ghaghi waddles slowly, but now nobody can step on her heels, as Ghigha
did before.
2) Ghagha does not walk where he usually does because he does not like
to walk in front of the nipping Ghughi.
3) Ghigha walks where he usually does.
4) The first gosling reaching the lake is going to be Ghagha, although
it is usually Ghaghi.
What was the original and what is the new order of the goslings in the
lineup?
Please, send your solutions to: