
North Dakota Mathematics Talent Search 20132014
The Department of
Mathematics at NDSU is happy to announce the start
of the annual North Dakota Mathematics Talent Search. The goals of the talent search are
to locate high school students in North Dakota and surrounding areas with a talent for
solving mathematical problems, to reward these students and their teachers for their efforts,
and to encourage these students to attend NDSU and major in the mathematical sciences or
engineering.
The Talent Search poses sets of challenging mathematical problems throughout the year
which will be posted as follows:
Interested students are strongly encouraged to send in solutions even if they only solve one
problem in a set; finding a good solution to a problem is always an achievement. The problems
do not require advanced mathematical knowledge  just creativity and a feeling or taste for
problem solving. It is not necessary to have participated in previous rounds. Everybody is welcome to send solutions to Round 3.
The students who submit a significant number of mathematically sound solutions for each
of the three rounds will be rewarded with various prizes, including a oneyear subscription
to a science/mathematics magazine of their choice. The best participants who decide to attend
NDSU and major in the mathematical sciences will also be rewarded with scholarships.
Please submit your solutions by email to
maria.alfonseca@ndsu.edu. Alternatively, solutions may be sent by regular mail to:
Talent Search
c/o Maria AlfonsecaCubero
Mathematics NDSU Dept.# 2750
PO BOX 6050
Fargo, ND 581086050
Please do not forget to include your name, postal address, school, and email address.
North Dakota Mathematics Talent Search Questions (20132014)
 Find z/(y+z), given that z/(x+y)=a and y/(x+z)=b.
 We write all the irreducible fractions p/q, where p,q are positive and q<100 in ascending order of value (for example, 4/9=0.444... comes after 2/5=0.4). Between which two fractions does 5/8 stand?
 The police department of a city is investigating a burglary. There are four suspects, A, B, C, and D. The police have established that the following facts are true:
 Fact 1: If both A and B are guilty, then C was their accomplice.
 Fact 2: If A is guilty, then either B or C were accomplices.
 Fact 3: If C is guilty, then D was his accomplice.
 Fact 4: If A is innocent, then D is guilty.
From these facts it can be proven that one of the four suspects is necessarily guilty. Who? (Note: An accomplice is considered guilty).
 Let ABCD be a rhombus (vertices are named consecutively, hence the two vertices closer to A are B and D). Consider all the points M on the plane of the rhombus, verifying that the sum of the angles AMB and CMD equals 180 degrees. Describe how such points are located.
 Prove: 4 a b <= (a + b)² <= (a + b)². Under what circumstances does equality hold?
 A family of four (father, mother, son, and daughter) are hiking in the evening and reach a shaky bridge when it is already dark. The bridge can hold no more than two people at a time, and those crossing need to have the lantern with them. There is just one lantern for the whole family. Suppose that it takes the son 1 minute to cross the bridge, the daughter 3 minutes, the father 8 minutes and the mother 10 minutes. Can the entire family cross the bridge in 20 minutes? If so, how? (When any two persons cross the bridge, their speed is equal to that of the slower one).

Address for US Postal Services
Letters / Billing / small PO Box type packages etc.
:
NDSU Mathematics Dept #2750
Attn: Melanie
PO Box 6050
Fargo ND 581086050

Address for UPS / Fed Ex / Large packages:
Department of Mathematics  #2750
Attn: Melanie
1210 Albrecht Boulevard Minard 412
North Dakota State University
Fargo ND 58102

Tel: 701.231.8171 Fax: 701.231.7598
Email: ndsu.math@ndsu.edu
Office Hours: Monday  Friday 8:00  5:00

   