ABACUS International Math Challenge
for
3rd and 4th graders
March, 2003
A.369. Three native American children are
practicing how to follow tracks of animals in the forest. Eagle-eye followed
the marks for a sixth of an hour, then Little Buffalo continued to lead
them for a fifth of a half an hour. After that it was Gray Wolf's turn,
who led his friends for four times as long as Little Buffalo did. At that
point they lost the tracks completely. How long did the three boys follow
the tracks all together?
A.370. The beautiful native American girl,
Speedy Deer, has 27 colored pearls in her hair. She has twice as many yellow
as red pearls. She has the same number of green and blue, but less then
the number of red pearls. How many of each color does she have?
A.371. The 5 sons of the chief are competing
in shooting arrows. Everybody has two arrows to shoot into the same circular
target. For each shot they can get a whole number of points anywhere between
1 and 10 depending on what part of the target they hit. All 10 shots hit
the target in an area with a different value. The scores were: Blue Lightning
11 points, Cat-eye 4 points, Big Buffalo 7 points, White Horn 16 points,
Arrow Head 17 points. How many points did they each get for each of their
shots?
A.372. White Smoke, the old wizard, put
some colored glass balls (18 yellow and 11 blue) in a leather bag. He randomly
takes balls out of the bag one by one. Magic happens when he pulls out two
yellow balls in a row. In the worst case scenario, how many balls does he
have to take out of the bag the most for this to happen?
A.373. Little Curious asked the Chief how
old the chief was. The old man said: "I have 5 sons and 2 daughters,
all of them were born in a nice progression of 3 and a half years apart
from one another. I was 24 when the oldest one was born, and my youngest
child just turned 13 recently." How old is the Chief?
A.374. The part of the totem pole above
ground has to be at least 4 m 80 cm long. For a safe installation one fourth
of the total length of the pole has to be under ground if the ground is
clay, and one third of the total length of the pole has to be under ground
if the ground is sandy. The tribe is planning to move from this clay ground
to a sandy ground. Do they need to carve a new totem pole if currently the
part of the pole above ground is 60 cm longer than necessary?
A.375. Great Hunter has a total of 104
arrows in his three arrow bags. If he takes out 18 from the first bag and
9 from the second bag, and puts one in the third bag, then all three bags
contain the same number of arrows. How many arrows were there originally
in each bag?
A.376. The representatives of the neighboring
tribes held a meeting to discuss strategies, then they set in a circle to
smoke the peace pipe. Chimacu, who was the fifth to smoke the pipe, was
sitting right across from his friend, Tomacu, who is going to be the 18th
to smoke. (Those who sit right across from each other have the same number
of people sitting between them on both sides. The pipe goes around the circle,
and everybody has one turn only.) How many representatives are sitting in
the circle?
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