POKHARA UNIVERSITY
Level: Bachelor
Semester – Fall
Programme: BE
Course: Problem Solving Technique
Year
: 2010
Full Marks: 100
Pass Marks: 45
Time
: 3hrs.
Candidates are required to give their answers in their own words as far
as practicable.
The figures in the margin indicate full marks.
Attempt all the questions.
1. a)
To number the pages of a large book, the printer uses 1890 digits.
How many pages are in the book?
b)
There are more adults than boys, more boys than girls, more girls
than families. If no family has fewer than 3 children, then what is the
least number of families that there could be?
c)
A right angled triangle has sides of length l, m and 10. Note that 10 is
not the hypotenuse, and that both l and m are integers. Find out the
pomble values of l and m such that with these three sides, right
angled triangles can be formed.
5
2. a)
Find out the last digit that contains in the evaluation of number
211111×388888+322222*299999?
8
b)
At the beginning of each class hour, each student shakes hands with
each of the other students and number of handshakes is 820. Find the
number of students.
3. a)
The lengths of the sides of a triangle form a sequence of positive
integers: n, n+1, n+2. The area of the triangle is 6. Find the sides of
the triangle.
b)
A circle of radius 1 is inscribed in an equilateral triangle of suitable
size. Then three more circles are inscribed between the first circle
and the two sides of the triangle near each vertex. The process
continues indefinitely, with progressively smaller circles. What is the
sum of the radii of all the circles?
4. a)
Suppose that you have 9 pearls. They all look the same, but 8 of them
have equal weight and one is different. The odd pearl is either lighter
or heavier; you do not know which. The only equipment that you
have at hand is a balance scale. How can you use the scale to find the
1
5
5
7
8
7
8
odd pearls? Your solution is to be an optimal solution.
b)
Draw a planar grid that is 18 squares wide and 10 squares high. How
many different nontrivial rectangles can be drawn, using the lines of
the grid to determine the boundaries?
7
5. a)
Solve the following crypto-arithmetic problem. In which, different
letters denote different integers; identical letters denote the same
integer.
8
ATOM = (A+TO+M)2
OR
WRONG
+W R O N G
RIGHT
b)
Explain why, if two positive real number sums to 100, then their
product cannot be 3000?
7
OR
Can we use each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 just once with
arithmetic operators to crate a collection of positive integers that sum to
100?
6. a)
An efficiency expert is doing study of a certain fast food restaurant.
She observes that a particular waiter drops 30% of all the hamburgers
that he serves. What is the probability that he will drop exactly 4 out
of 10?
b)
You have a piece of paper with a circle of radius between 2 inch and
4 inch drawn on it. You also have a plastic square of side 10 inches.
You have no ruler and no compass. How can you find the center of
the circle?
c)
On Friday evening the weatherperson predicts 50% chance of rain on
Saturday and 50% chance of rain on Sunday. What is the probability
that it will rain at some time this weekend?
7. Write short notes on: (Any Two)
a) Recreational Math
b) Crypto arithmetic problems as constraint satisfaction problem
c) Problems of Parity Issues
2
3×5
2×5