ABACUS International Math Challenge
for
5th and 6th graders
December, 2007
B.609. You can cut a 6cm x 8cm piece of
paper into seven squares without any left-over, so that the side of each
square is a whole number of cm, only two ways. What is the total length
of the cuts in each case?
B.610. The sum of the ages of Henry and
his father is 33 years. 15 years from now Henry is going to be half as old
as his mother, and 18 years from now he is going to be half as old as his
father. How old are Henry and and his parents now?
B.611. If you continued the diagrams on
the following picture, how many little squares would the 30th diagram contain?
B.612. Rita Half drew the following polygon
into her notebook. She states that she can draw a straight segment from
any grid point on the perimeter of the polygon, so that the segment would
half the area of the polygon, and that the other end of the segment is a
grid point on the perimeter, too. Is Rita correct, or not?
B.613. Find the smallest positive whole
number in which the product of the digits is 648, and any two neighboring
digits are different.
B.614. James Bond is preparing to defuse
a time-bomb. There are four kinds of wires in the mechanism: red, yellow,
blue and green. He has to cut all the wires in order to defuse the bomb,
but he can cut only one wire at a time. He learned that only one event causes
the bomb to blow up, but he cannot remember which one: if you cut the red
wire before the yellow, or if you cut the blue wire before the red. Find
all possible ways to defuse to bomb without blowing it up.
B.615. There are two strange people living
in Nevermind country: Peter, who lies on every Monday, Tuesday and Wednesday,
but says the truth on all the other days; and Paul, who lies on every Thursday,
Friday and Saturday, but tells the truth on all the other days. One day
they said:
Peter: "Yesterday I had a lying day."
Paul: "Yesterday I had a lying day, too."
What day of the week was this on?
B.616. Tom is twice as old as Jerry, but
4 years ago Tom was three times as old as Jerry. How old are they now?