ABACUS International Math Challenge
for
5th and 6th graders
October, 2005
B.497. The card game called "Fifteen"
is played by using a deck of 52 card: every card has a color (red, green,
yellow or blue) and there is a number on it between from 1 to 13 (each number
occurring only once on each color card). Each played gets 5 cards. If a
player finds in his hands a few cards whose values add up to fifteen then
the player gets 2 points. If the player can do this in different ways (using
different cards), then the player receives 2 points for each way. If all
the cards of a "fifteen" are the same color, then the player receives
4 (not 2) points for that "fifteen". How many points do you receive
if you have in your hands:
a) a red 5, a green 5, a yellow 5, a blue 5, and a green 10 card;
b) a yellow 10, a green 10, a yellow 3, a red 2 and a yellow 2?
B.498. Let's introduce a new unit of length:
1 entime = 1/2 centimeter. A matchbox is 10 entime long, 7 entime
wide and 3 entime high. At most how many such matchboxes can you put in
a 20 entime x 21 entime x 16 entime size box?
B.499. Write all the whole numbers from
0 to 11 into the small squares of the diagram so that the sum of the fields
on each side of the big square is 18. Give three different such arrangements
of the numbers. (Two arrangements are considered to be different if one
cannot be moved into the other by rotation and/or reflection.)
B.500. A science magazine had the following
yearly subscription fees:
If you order 1 4 copies per issue to the same address then the
price is $21/copy.
If you order 5 9 copies per issue then the price is $19/copy.
If you order 10 or more copies per issue then the price is $17/copy.
Are there any numbers of copies that are not worth ordering because
you kind of lose money doing so?
B.501. Sometimes you can see interesting
things looking at the date of a day. How many days are there in a year when
the number of the day is divisible by the number of the month?
B.502. Anne, Bea, Cecilia and Dori found
a secret staircase leading to the attic. Nobody used it for a long time,
so it was covered with dust. The girls ran down on it as fast as they could:
Anne stepped on every other step, Bea used every 3rd step, Cecilia used
every 4th step, and Dori used only every 5th step. There are a total of
40 steps on this staircase, and everybody started from the step on top.
How many steps have still no footprints on them after the girls ran down?
B.503. There are 11 floors in a building.
(10 floors above the ground floor.) There is an automatic elevator in the
building which starts from the ground floor and on its way up it stops on
every floor. Once it stopped on the top floor, it starts to come down and
stops on every floor again. It takes the elevator 8 seconds to get from
one floor to the next, and it stops on each floor for 12 seconds. On the
ground floor it stays for an additional 1 minute (a total of 72 seconds).
At 8:00 am the elevator starts working with a 1 minute waiting time on the
ground floor, and then it starts to go up. What is the first time after
4:00 pm when the elevator reaches the ground floor? How many round trips
did the elevator make from 8:00 am till that time?
B.504. If Andrew gave $3 to Ben, and then
Ben gave $5.60 to Colin, and then Colin gave $3.70 to Andrew then everybody
had $20. How much money do each of the boys have?