ABACUS International Math Challenge
for
3rd and 4th graders
November, 2008
A.657. Draw a triangle and a quadrilateral
so that their sides would have
a) 1
b) 3
c) 5
d) 6
e) 7 mutual points.
A.658. Could the sum of the squares of
two consecutive whole numbers be the square of a whole number?
A.659. How many pieces can you possible
get if you cut a rectangular based column by three plane cuts?
A.660. At a village carnival you can buy
local musical instruments for their local currency, which is dings and dongs.
You can buy one ding for $5, and one dong is worth 3 dings. A wooden recorder
and a clay whistle together are worth the same as three mouth harps. Four
wooden recorders and three mouth harps together are worth the same as two
clay whistles. What is the price of each instrument in dollars if you can
buy a wooden recorder for 4 dongs and 2 dings?
A.661. Find the smallest prime number that
is the sum of three different prime numbers.
A.662. At the gingerbread stand there are
three different figures you can buy: heart, doll and soldier. Every third
figure is a heart, every other heart has a mirror in the middle of it. Every
fifth figure is a doll. I counted a total of 90 figures. How many of them
is a heart with a mirror in the middle, and how many of them is a soldier?
A.663. Inga bought 5 meters of linen and
2 meters of silk for $36.60. Eva bought 7 meters of linen and 4 meters of
silk for $67.00. Veronica bought 3 meters of linen and 3 meters of silk.
How much change did she get back from $100.00?
A.664. You may use a red and a blue pen,
and you may write the digits 1, 2, or 3. How many different 6-digit numbers
can you write down if the numbers must contain every digit in red and in
blue, but no identical colors and no identical digits can be written next
to one another?
Please, send your solutions to:
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