1. A foundation has allocated a certain amount of money for
1st, 2nd and 3rd prizes in a competition. The
money is divided in the ratio of 3：2
where the larger amount is for the 1st prize and the smaller amount
is divided again in the ratio of 3：2
for the 2nd and 3rd prizes respectively. It becomes known
that the 3rd prize is $3300 less than the first prize. How much is
the 2nd prize?
2. Three man and three children arrive at the river where
there is a small boat that will hold one adult or two children. What is the
minimum number of trips across the river in either direction to get the family
across?
3. Mr. Sun has a broken calculator. When just turned on, it
displays 0. If the + key is pressed, it adds 35. If the－key is pressed, it subtracts 35. If the × key
is pressed, it adds 91. If the ÷ key is pressed, it subtracts 91. The
other keys do not function. Mr. Sun turns the calculator on. What is the number
closest to 2005 that he can get using this calculator?
4. There are 500 unit cubes. As many of these cubes as
needed are glued together to form the largest possible cube which looks solid
from any point on the outside but is hollow inside. What is the side length of
the largest cube?
5. What is the ratio of the shaded square to that of the largest
square shown in the diagram?
6. A three-digit number N leaves remainder 3 when divided
by 7, remainder 5 when divided by 11 and remainder 8 when divided by 17. What
is the number N ?
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