International Mathematics
TOURNAMENT OF THE TOWNS
Senior O-Level Paper
Fall 2007.
1. Pictures are taken of 100 adults and 100 children, with one adult and one child in each, the
adult being the taller of the two. Each picture is reduced to k1 of its origi

International Mathematics
TOURNAMENT OF THE TOWNS
Senior A-Level Paper1
Spring 2007.
1. A, B, C and D are points on the parabola y = x2 such that AB and CD intersect on the
y-axis. Determine the x-coordinate of D in terms of the x-coordinates of A, B and

International Mathematics
TOURNAMENT OF THE TOWNS
Senior A-Level Paper
Spring 2010.1
1. Is it possible to divide the lines in the plane into pairs of perpendicular lines so that every
line belongs to exactly one pair?
2. Alex has a piece of cheese. He cho

Seniors
(Grades 11 and up)
International Mathematics
TOURNAMENT OF THE TOWNS
A-Level Paper
Spring 2003.
1 [4] A triangular pyramid ABCD is given. Prove that R/r > a/h, where R is the radius of the
circumscribed sphere, r is the radius of the inscribed sph

INTERNATIONAL MATHEMATICS TOURNAMENT OF
TOWNS
Senior O-Level, Spring 2014.
1. Inspector Gadget has 36 stones with masses 1 gram, 2 grams, . . . , 36
grams. Doctor Claw has a superglue such that one drop of it glues two
stones together (thus two drops glue

International Mathematics
TOURNAMENT OF THE TOWNS
Senior O-Level Paper
Fall 2009.1
1. A 7-digit passcode is called good if all digits are different. A safe has
a good passcode, and it opens if seven digits are entered and one of
the digits matches the cor

International Mathematics
TOURNAMENT OF THE TOWNS
Senior O-Level Paper
Spring 2010.1
1. Bananas, lemons and pineapples are being delivered by 2010 ships. The number of bananas
in each ship is equal to the total number of lemons in the other 2009 ships, an

Seniors
(Grades 11 and up)
International Mathematics
TOURNAMENT OF THE TOWNS: SOLUTIONS
A-Level Paper
1
Spring 2003.
Solution 1. The longest edge of the pyramid is a chord of the circumscribed sphere and thus it does not exceed diameter of the sphere:
a 2

EE100 Fall 2008
Guest Lecture 2: Mesh and Nodal
Analysis
Bharathwaj Muthuswamy
NOEL Laboratory
151M Cory Hall
Department of EECS
University of California, Berkeley
mbharat@cory.eecs.berkeley.edu
http:/nonlinear.eecs.berkeley.edu
Slide Number: 1

Seniors
(Grades 11 and up)
International Mathematics
TOURNAMENT OF THE TOWNS
O-Level Paper
Spring 2003.
1 [3] 2003 dollars are placed into N purses, and the purses are placed into M pockets. It is known
that N is greater than the number of dollars in any

Juniors
(Grades up to 10)
International Mathematics
TOURNAMENT OF THE TOWNS
A-Level Paper
Spring 2003.
1 [4] Johnny writes down quadratic equation
ax2 + bx + c = 0
with positive integer coefficients a, b, c. Then Pete changes one, two, or none + signs to

International Mathematics
TOURNAMENT OF THE TOWNS
Senior A-Level Paper
Fall 2008.
1. A standard 8 8 chessboard is modified by varying the distances between parallel grid lines,
so that the cells are rectangles which are not necessarily squares, and do not

International Mathematics
TOURNAMENT OF THE TOWNS
Senior A-Level Paper
Spring 2011.
1. Baron Munchausen has a set of 50 coins. The mass of each is a distinct positive integer not
exceeding 100, and the total mass is even. The Baron claims that it is not p