MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - Other Middle and High School Contests
SDML/SDMO Contests
SDML (Middle School)
2007-2008 SDML (Middle School)
2007-2008 SDML (Middle School)
Part of
SDML (Middle School)
Subcontests
(8)
8
1
Hide problems
Square paper lengths
A square sheet of paper that measures
18
18
18
cm on a side has corners labeled
A
A
A
,
B
B
B
,
C
C
C
, and
D
D
D
in clockwise order. Point
B
B
B
is folded over to a point
E
E
E
on
A
D
‾
\overline{AD}
A
D
with
D
E
=
6
DE=6
D
E
=
6
cm and the paper is creased. When the paper is unfolded, the crease intersects side
A
B
‾
\overline{AB}
A
B
at
F
F
F
. Find the number of centimeters in
F
B
FB
FB
.
7
1
Hide problems
Integers on marbles
Each of the first
150
150
150
positive integers is painted on a different marble, and the
150
150
150
marbles are placed in a bag. If
n
n
n
marbles are chosen (without replacement) from the bag, what is the smallest value of
n
n
n
such that we are guaranteed to choose three marbles with consecutive numbers?
6
1
Hide problems
Factorial ending in 43 zeros!
Find the smallest positive integer
k
k
k
such that
k
!
k!
k
!
ends in at least
43
43
43
zeroes.
5
1
Hide problems
I was jogging when a fly started flying back and forth...
Maria and Joe are jogging towards each other on a long straight path. Joe is running at
10
10
10
mph and Maria at
8
8
8
mph. When they are
3
3
3
miles apart, a fly begins to fly back and forth between them at a constant rate of
15
15
15
mph, turning around instantaneously whenever it reachers one of the runners. How far, in miles, will the fly have traveled when Joe and Maria pass each other?
4
1
Hide problems
Flyfishing Club Officers
The Flyfishing Club is choosing officers. There are
23
23
23
members of the club.
14
14
14
of them are boys and
9
9
9
are girls. In how many ways can they choose a President and a Vice President if one of them must be a boy and the other must be a girl (either office can be held by the boy or the girl)?
3
1
Hide problems
Sum of consecutive integers adding to 190
If
n
n
n
is a positive integer such that
1
+
2
+
3
+
⋯
+
n
=
190
1+2+3+\cdots+n=190
1
+
2
+
3
+
⋯
+
n
=
190
, then what is
n
n
n
?
2
1
Hide problems
Positive divisors of 200
How many positive divisors does
200
200
200
have?
1
1
Hide problems
Algebraic expression
Find
x
x
x
if
1
+
3
x
2
−
2
x
=
7
\frac{1+\frac{3}{x}}{2-\frac{2}{x}}=7
2
−
x
2
1
+
x
3
=
7
.