ABACUS International Math Challenge
for
3rd and 4th graders
April, 2000
A.185. Can you connect the dots on the
following diagram with 5 straight lines without lifting your pencil?
Jonathan Dornian
A.186. Find the smallest positive whole
number in which the product of the digits is 1296.
A.187. A horse trader bought a horse for
$600 on the market, which he later sold for $700. A month later he saw the
same horse on the market and bought it for $800 this time. Soon he sold
it again for $900. Did the trader lose or gain money on these transactions
overall? How much was his gain or loss?
A.188. The dwarves together bought a barrel
of syrup. If everybody gave in $8 then they have $3 left over, but if everybody
gave in $7 then they would need $4 more. How many dwarves are there and
how much does the barrel of syrup cost?
A.189. Mark 5 fields on a 5x5 grid, so
that there are no two marks in the same row, or same column, or same diagonal,
or on the same line parallel to any of the diagonals.
A.190. Create a 3x3 magic square from the
following numbers:
1, 7, 13, 31, 37, 43, 61, 67, and 73
(In a magic square the sum of the numbers in each row, column and diagonal
is the same.)
A.191. In an Amusement Park there is a
booth where you have to knock down cans with cloth-balls. A can will fall
down if you hit it, or if at least one of its supporting cans falls down.
At least how many cans do you have to hit (and which ones) in order for
the sum of the numbers on the cans fallen to be exactly 50?
A.192. The size and the coloring of three
dice are the same. There is a different color on each of the 6 sides. Doc,
Happy and Grumpy each have a die in their hands and make the following statements
about the colors of the three sides meeting in one vertex that they see:
Doc: "Blue, white, yellow."
Happy: "Orange, blue, red."
Grumpy: "Green, orange, white."
What color is facing white?
Please, send your solutions to: