MATH-GENII
Mathematics quiz
Round II
LEVEL I
1.THIS LEVEL COMPRISES 5 QUESTIONS
2. AT MAX TWO ANSWERS WILL BE HEARD FOR EACH
QUESTION
.
3.FIRST ATTEMPT
: PLUS 10 MINUS 5
SECOND ATTEMPT : PLUS 5 MINUS 5
4.MAX TIME LIMIT 4MIN (APPROX).
QUESTION- 1
The police commissioner hired a mathematician to help
at a crime scene. At the scene were between 100 and 200
glasses of wine. Exactly one glass was poisoned. The
police lab could test any sampling for poison. A group of
glasses could be tested simultaneously by mixing a
sample from each glass. The police commissioner desires
only to minimize the maximum possible tests required to
determine which exact glass was poisoned. The
mathematician started by asking a detective to select a
single glass at random for testing. "Wouldn't that waste a
test?", the detective asked. "No, besides I'm in a gambling
mood.", the mathematician replied. How many glasses
were there?
QUESTION- 2
Find the value of the infinite product
QUESTION- 3
You are a cook in a remote area with no clocks or
other way of keeping time other than a 4 minute
hourglass and a 7 minute hourglass. You do have a
stove however with water in a pot already boiling.
Somebody asks you for a 9 minute egg, and you
know this person is a perfectionist and will be able
to tell if you undercook or overcook the eggs by
even a few seconds. What is the least amount of
time it will take to prepare the egg?
QUESTION- 4
Five marbles of various sizes are placed in a conical
funnel. Each marble is in contact with the adjacent
marble(s). Also, each marble is in contact all around the
funnel wall.
The smallest marble has a radius of 8mm.
The largest marble has a radius of 18mm.
What is the radius of the middle marble?
QUESTION- 5