2017 UNM-PNM Statewide High School Mathematics Contest II Problems
UNM - PNM STATEWIDE MATHEMATICS CONTEST XLIX. February 4, 2017. Second Round. Three Hours
Contents
Problem 1
What are the last two digits of ?
Problem 2
Suppose , and
all denote distinct digits from
to
. If
, what are
, and
?
Problem 3
Let and
.
(a) Determine and
.
(b) Denote .
Determine all the functions in the set
or
for some
a whole number
.
Problem 4
Find a second-degree polynomial with integer coefficients, , such that
, and
are perfect squares, but
is not.
Problem 5
Find all real triples which are solutions to the system:
Problem 6
There are stacks of
coins. Each of the coins in
of the
stacks weighs
grams each. Suppose the coins in the remaining stack each weigh
grams. You are given one time access to a precise digital scale. Devise a plan to weigh some coins in precisely one weighing to determine which pile has the lighter coins.
Problem 7
Find a formula for
$sum_{k=0}^{$ (Error compiling LaTeX. Unknown error_msg)\lceil \frac{n}{4} \rceil } binom{n}{4k}n$.