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 th
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-coo
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
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
cir
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 dr
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 d
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
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
EE100 Fall 2008
Guest Lecture 2: Mesh and Nodal
Analysis
Bharathwaj Muthuswamy
NOEL Laboratory
151M Cory Hall
Department of EECS
University of California, Berkeley
[email protected]
http:
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 kno
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
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 r
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