Maurer, Stephen B.

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Swarthmore College 
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Mathematics & Statistics Faculty Works Mathematics & Statistics 
9-1-1986 
Keane Leads US Olympiad Team To 1st Place Tie With USSR 
Stephen B. Maurer 
Swarthmore College, smaurer1@swarthmore.edu 
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Recommended Citation 
Stephen B. Maurer. (1986). "Keane Leads US Olympiad Team To 1st Place Tie With USSR". FOCUS. 
Volume 6, Issue 4. 1-2. 
https://works.swarthmore.edu/fac-math-stat/134 
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THE NEWSLETTER OF THE MATHEMATICAL ASSOCIATION OF AMERICA
VOLUME 6 NUMBER 4 September 1986
Keane Leads US Olympiad Team to 1st Place Tie with USSR
Stephen B. Maurer
S coring 41 out of a possible 42, Joseph Keane of Pitts-burgh, Pennsylvania, led the US team of 6 to a winner's
tie with Russia in the 27th International Mathematical Olym-
piad, held July 9-10 in Warsaw. Both countries scored 203,
followed by West Germany (196), China (177), East Germany
(172) and Romania (171).
The Russians had 2 perfect papers (6 problems, 7 points
each) and the Hungarians had one, but Keane was the only
participant of the 210 from 37 countries to receive a Special
Award for a particularly elegant solution. The problem he
received it for is given at the end of this article. (Finding his
solution is left to the reader!)
The US was the only one of last year's top 5 nations to
make it to the top 5 this year. Last year the US was 2nd (180)
behind Romania (201). The USSR was 6th in 1985 and 1st in
1984.
Keane received a Gold Medal, as did his teammates David
Grabiner of Claremont, California (score 36), and Jeremy
Kahn of New York City (35). The other team members all
received Silver: Hohn Overdeck of Columbia, Maryland (32),
I
USAMO winners are greeted by Dr. Erich Bloch, Director of
NSF. The winners from left to right are: Ravi D. Vakil of
Ontario, Eric K. Wepsic of Massachussetts, David J. Grabi-
ner of California, William P. Cross of Michigan, followed by
Dr.Bloch and then Joseph G. Keane of Pennsylvania, Darien
G. Lefkowitz and Jeremy A. Kahn, both of New York, and
John J. Bulten of Oklahoma.
Darien Lefkowitz of New York City (30), and William Cross of
Kalamazoo, Michigan (29).
Notable this year was the strong showing by The People's
Republic of China. This was only the 2nd time they partici-
pated, and the first time they fielded a full team. Another
highlight was the Bronze Medal performance of a 10-year
old from Australia.
The US team was again coached by Professor Cecil Rous-
seau of Memphis State University and Gregg Patruno of
Columbia and the First Boston investment firm.
All the US team members but Kahn were seniors, an unusual
situation. Thus, it will be challenging to build for next year's
IMO in Cuba.
The US team was chosen based on the USA Mathematical
Olympiad, held on April 22, and on additional work at a
rigorous 4-week Training Session at the US Naval Academy.
The highest scoring USAMO participants, and other high
scoring nonseniors, were invited. 5 of the 6 students chosen
for the IMO team were USAMO Winners (top 8); the 6th, John
Overdeck, was a Winner in 1985. The other Winners of the
1986 USAMO were John Bulten of Tulsa, Ravi Vakil of Isling-
ton, Ontario, and Eric Wepsic of Boston. All 8 Winners were
honored at elegant ceremonies in Washington, D.C., on June
2-3. The Greitzer/Klamkin Award, for the very top USAMO
score, went to Keane-for the 2nd year in a row.
The success of the US team is partly the result of a broad-
based program to discover and encourage mathematical
talent. The USAMO is the third in the series of high school
exams sponsored by the MAA and 6 other mathematics soci-
eties. Joe Keane also received the top score in the 2nd, the
American Invitational Mathematics Examination, sharing a
perfect score of 15 with Robert Southworth of Winchester,
(continued on page 2)
MAA Sections Featured in
Center Section
Preliminary Announcement
of 70th Annual Meeting, page 3
Fields Medalists and leM, page 5
2 FOCUS September 1986
Keane (continued from page 1)
MA. For further information on the 1986 AIME, and on the
1st exam (AHSME), see page iii of the May-June FOCUS;
however, these results were erroniously attributed to 1985.
MAA members can do much to strengthen this program by
encouraging local schools to participate. An IMO/USAMO
problems-solutions pamphlet, and similar pamphlets for the
AIME and AHSME, are available. Members may contact Pro-
fessor Walter E. Mientka, 917 Oldfather Hall, University of
Nebraska, Lincoln, NE, 68588-0322 for prices.
Here is the problem that Joseph Keane solved so elegantly:
1986 IMO, Problem 3 (submitted by E. Germany): To each
vertex of a regular pentagon an integer is assigned in such
a way that the sum af all the five numbers is positive. If three
consecutive vertices are assigned the numbers x, y,z, respec-
tively, and y<O then the following operation is allowed: the
numbers x, y, z, are replaced by x + y, - y, z + y respectively.
Such an operation is performed repeatedly as long as at least
one of the five numbers is negative. Determine whether this
procedure necessarily comes to an end after a finite number
of steps. (After participants asked for clarification it was
announced that "necessarily" means regardless of which
negative number y is operated on when there is a choice.)
'.CUI
FOCUS (ISSN 0731-2040) is published by the Mathematical
Association of America, 1529 Eighteenth Street, N.W., Wash-
ington, D.C. 20036, six times a year: January-February, March-
April, May-June, September, October, November-December.
Editor: Peter Renz, MAA Associate Director.
Associate Editors: Donald J. Albers, Menlo College; David
Ballew, South Dakota School of Mines and Technology; Wil-
liam G. Chinn, City College of San Francisco; Stephen B.
Maurer, Swarthmore College.
Chairman of the MAA Newsletter Editorial Committee:
Ronald M. Davis, Northern Virginia Community College.
Readers are invited to submit articles, announcements, or
Letters to the Editor for possible publication in FOCUS. All
materials should be sent to the Editor at the MAA Headquar-
ters in Washington, D.C.
The annual subscription price for FOCUS to individual mem-
bers of the Association is $1, included as a part of the annual
dues. Annual dues for regular members (exclusive of annual
subscription prices for MAA journals) are $22. Student, unem-
ployed, emeritus, and family members receive a 50% discount;
new members receive a 30% discount for the first two years
of membership.
Copyright by the Mathematical Association of America
(Incorporated), 1986. Educational institutions may reproduce
articles from this publication for their own use, but not for
sale, provided that the following citation is used: "Reprinted
with permission from FOCUS, the Newsletter of the Mathe-
matical Association of America. Copyright by the Mathe-
matical Association of America (Incorporated), 1986."
Second-class postage paid at Washington, D.C. and additional
mailing offices.
Postmaster: Send address changes to Membership/Subscrip-
tions Department, Mathematical Association of America, 1529
Eighteenth Street, N.W., Washington, D.C. 20036.
Printed in the United States of America.
Lynn Arthur Steen, SI Olaf College
Proposal Pressure
In recent years the National Science Foundation's support
for educational activities has had a very bimodal distribution,
with strong programs at the pre-collegiate and post-graduate
levels but virtually no support for undergraduate activities.
Moreover, all existing programs for mathematics education
and mathematics research are seriously inadequate when
measured by the needs of the mathematics community. As
a consequence, many mathematicians-especially many
college mathematics faculty-have lost interest in trying to
get NSF support either for themselves, for their departments,
or for their students.
That's bad for at least two reasons. Those who don't apply
stand no chance of receiving an award, so the total support
for mathematics begins to dwindle. Moreover, since there is
insufficient "proposal pressure" from mathematics, future
budgets for mathematics are also placed in jeopardy, espe-
cially when put in competition against other fields where
proposers inundate NSF with strong requests.
Consider these examples selected from among the very
few NSF programs that bear directly on undergraduate math-
ematics. Last year only 25 mathematics students received
NSF graduate fellowships out of 500 total awards. And despite
widespread need for increasing computer resources in
undergraduate mathematics, only 2 out of 200 awards made
in the College Science Instrumentation Program (CSIP) went
to mathematics curricular projects.
It is well known that mathematics students score better on
the Graduate Record Examination than do most other stu-
dents who take that exam. Even after suitable normalization
to account for different pools of students taking different
exams, mathematics GRE scores average one standard
deviation higher than those in chemistry, biology, computer
science, or economics.
Then why don't more mathematics students receive NSF
Graduate Fellowships? Because not enough of them apply.
To promote fairness in administration, and because of the
difficulty of making cross-disciplinary comparisons, awards
in different fields are generally made in proportion to appli-
cations. Last year only about 100 students-about 1 in 40 of
those applying to graduate school-applied for an NSF Grad-
uate Fellowship in mathematics.
There are many possible reasons for the shortage of math-
ematics applicants in the Graduate Fellowship competition:
low interest in mathematics graduate school; reputation that
only geniuses can get a Graduate Fellowship; insufficient
encouragement from advisors and departments. The fact is,
however, that both applications and awards are low even in
proportion to the number of students entering graduateschool,
and as the GRE scores show, graduate-school-bound math-
ematics students will quite likely fare well in head-to-head
competition with other students. The crucial missing ingre-
dient is faculty encouragement.
A similar problem of weak proposal pressure exists in the
CSIP program, although almost certainly for different rea-


Keane Leads US Olympiad Team To 1st Place Tie With USSR

Swarthmore College Works Mathematics & Statistics Faculty Works Mathematics & Statistics 9-1-1986 Keane Leads US Olympiad Team To 1st Place Tie With USSR Stephen B. Maurer Swarthmore College, smaurer1@swarthmore.edu This work is brought to you for free and open access by . It has been accepted for inclusion in Mathematics & Statistics Faculty Works by an authorized administrator of Works. For more information, please contact myworks@swarthmore.edu. Follow this and additional works at: https://works.swarthmore.edu/fac-math-stat  Part of the Discrete Mathematics and Combinatorics Commons Let us know how access to these works benefits you  Recommended Citation Stephen B. Maurer. (1986). "Keane Leads US Olympiad Team To 1st Place Tie With USSR". FOCUS. Volume 6, Issue 4. 1-2. https://works.swarthmore.edu/fac-math-stat/134 THE NEWSLETTER OF THE MATHEMATICAL ASSOCIATION OF AMERICAVOLUME 6 NUMBER 4 September 1986Keane Leads US Olympiad Team to 1st Place Tie with USSRStephen B. MaurerS coring 41 out of a possible 42, Joseph Keane of Pitts-burgh, Pennsylvania, led the US team of 6 to a winner'stie with Russia in the 27th International Mathematical Olym-piad, held July 9-10 in Warsaw. Both countries scored 203,followed by West Germany (196), China (177), East Germany(172) and Romania (171).The Russians had 2 perfect papers (6 problems, 7 pointseach) and the Hungarians had one, but Keane was the onlyparticipant of the 210 from 37 countries to receive a SpecialAward for a particularly elegant solution. The problem hereceived it for is given at the end of this article. (Finding hissolution is left to the reader!)The US was the only one of last year's top 5 nations tomake it to the top 5 this year. Last year the US was 2nd (180)behind Romania (201). The USSR was 6th in 1985 and 1st in1984.Keane received a Gold Medal, as did his teammates DavidGrabiner of Claremont, California (score 36), and JeremyKahn of New York City (35). The other team members allreceived Silver: Hohn Overdeck of Columbia, Maryland (32),IUSAMO winners are greeted by Dr. Erich Bloch, Director ofNSF. The winners from left to right are: Ravi D. Vakil ofOntario, Eric K. Wepsic of Massachussetts, David J. Grabi-ner of California, William P. Cross of Michigan, followed byDr.Bloch and then Joseph G. Keane of Pennsylvania, DarienG. Lefkowitz and Jeremy A. Kahn, both of New York, andJohn J. Bulten of Oklahoma.Darien Lefkowitz of New York City (30), and William Cross ofKalamazoo, Michigan (29).Notable this year was the strong showing by The People'sRepublic of China. This was only the 2nd time they partici-pated, and the first time they fielded a full team. Anotherhighlight was the Bronze Medal performance of a 10-yearold from Australia.The US team was again coached by Professor Cecil Rous-seau of Memphis State University and Gregg Patruno ofColumbia and the First Boston investment firm.All the US team members but Kahn were seniors, an unusualsituation. Thus, it will be challenging to build for next year'sIMO in Cuba.The US team was chosen based on the USA MathematicalOlympiad, held on April 22, and on additional work at arigorous 4-week Training Session at the US Naval Academy.The highest scoring USAMO participants, and other highscoring nonseniors, were invited. 5 of the 6 students chosenfor the IMO team were USAMO Winners (top 8); the 6th, JohnOverdeck, was a Winner in 1985. The other Winners of the1986 USAMO were John Bulten of Tulsa, Ravi Vakil of Isling-ton, Ontario, and Eric Wepsic of Boston. All 8 Winners werehonored at elegant ceremonies in Washington, D.C., on June2-3. The Greitzer/Klamkin Award, for the very top USAMOscore, went to Keane-for the 2nd year in a row.The success of the US team is partly the result of a broad-based program to discover and encourage mathematicaltalent. The USAMO is the third in the series of high schoolexams sponsored by the MAA and 6 other mathematics soci-eties. Joe Keane also received the top score in the 2nd, theAmerican Invitational Mathematics Examination, sharing aperfect score of 15 with Robert Southworth of Winchester,(continued on page 2)MAA Sections Featured inCenter SectionPreliminary Announcementof 70th Annual Meeting, page 3Fields Medalists and leM, page 52 FOCUS September 1986Keane (continued from page 1)MA. For further information on the 1986 AIME, and on the1st exam (AHSME), see page iii of the May-June FOCUS;however, these results were erroniously attributed to 1985.MAA members can do much to strengthen this program byencouraging local schools to participate. An IMO/USAMOproblems-solutions pamphlet, and similar pamphlets for theAIME and AHSME, are available. Members may contact Pro-fessor Walter E. Mientka, 917 Oldfather Hall, University ofNebraska, Lincoln, NE, 68588-0322 for prices.Here is the problem that Joseph Keane solved so elegantly:1986 IMO, Problem 3 (submitted by E. Germany): To eachvertex of a regular pentagon an integer is assigned in sucha way that the sum af all the five numbers is positive. If threeconsecutive vertices are assigned the numbers x, y,z, respec-tively, and y<O then the following operation is allowed: thenumbers x, y, z, are replaced by x + y, - y, z + y respectively.Such an operation is performed repeatedly as long as at leastone of the five numbers is negative. Determine whether thisprocedure necessarily comes to an end after a finite numberof steps. (After participants asked for clarification it wasannounced that "necessarily" means regardless of whichnegative number y is operated on when there is a choice.)'.CUIFOCUS (ISSN 0731-2040) is published by the MathematicalAssociation of America, 1529 Eighteenth Street, N.W., Wash-ington, D.C. 20036, six times a year: January-February, March-April, May-June, September, October, November-December.Editor: Peter Renz, MAA Associate Director.Associate Editors: Donald J. Albers, Menlo College; DavidBallew, South Dakota School of Mines and Technology; Wil-liam G. Chinn, City College of San Francisco; Stephen B.Maurer, Swarthmore College.Chairman of the MAA Newsletter Editorial Committee:Ronald M. Davis, Northern Virginia Community College.Readers are invited to submit articles, announcements, orLetters to the Editor for possible publication in FOCUS. Allmaterials should be sent to the Editor at the MAA Headquar-ters in Washington, D.C.The annual subscription price for FOCUS to individual mem-bers of the Association is $1, included as a part of the annualdues. Annual dues for regular members (exclusive of annualsubscription prices for MAA journals) are $22. Student, unem-ployed, emeritus, and family members receive a 50% discount;new members receive a 30% discount for the first two yearsof membership.Copyright by the Mathematical Association of America(Incorporated), 1986. Educational institutions may reproducearticles from this publication for their own use, but not forsale, provided that the following citation is used: "Reprintedwith permission from FOCUS, the Newsletter of the Mathe-matical Association of America. Copyright by the Mathe-matical Association of America (Incorporated), 1986."Second-class postage paid at Washington, D.C. and additionalmailing offices.Postmaster: Send address changes to Membership/Subscrip-tions Department, Mathematical Association of America, 1529Eighteenth Street, N.W., Washington, D.C. 20036.Printed in the United States of America.Lynn Arthur Steen, SI Olaf CollegeProposal PressureIn recent years the National Science Foundation's supportfor educational activities has had a very bimodal distribution,with strong programs at the pre-collegiate and post-graduatelevels but virtually no support for undergraduate activities.Moreover, all existing programs for mathematics educationand mathematics research are seriously inadequate whenmeasured by the needs of the mathematics community. Asa consequence, many mathematicians-especially manycollege mathematics faculty-have lost interest in trying toget NSF support either for themselves, for their departments,or for their students.That's bad for at least two reasons. Those who don't applystand no chance of receiving an award, so the total supportfor mathematics begins to dwindle. Moreover, since there isinsufficient "proposal pressure" from mathematics, futurebudgets for mathematics are also placed in jeopardy, espe-cially when put in competition against other fields whereproposers inundate NSF with strong requests.Consider these examples selected from among the veryfew NSF programs that bear directly on undergraduate math-ematics. Last year only 25 mathematics students receivedNSF graduate fellowships out of 500 total awards. And despitewidespread need for increasing computer resources inundergraduate mathematics, only 2 out of 200 awards madein the College Science Instrumentation Program (CSIP) wentto mathematics curricular projects.It is well known that mathematics students score better onthe Graduate Record Examination than do most other stu-dents who take that exam. Even after suitable normalizationto account for different pools of students taking differentexams, mathematics GRE scores average one standarddeviation higher than those in chemistry, biology, computerscience, or economics.Then why don't more mathematics students receive NSFGraduate Fellowships? Because not enough of them apply.To promote fairness in administration, and because of thedifficulty of making cross-disciplinary comparisons, awardsin different fields are generally made in proportion to appli-cations. Last year only about 100 students-about 1 in 40 ofthose applying to graduate school-applied for an NSF Grad-uate Fellowship in mathematics.There are many possible reasons for the shortage of math-ematics applicants in the Graduate Fellowship competition:low interest in mathematics graduate school; reputation thatonly geniuses can get a Graduate Fellowship; insufficientencouragement from advisors and departments. The fact is,however, that both applications and awards are low even inproportion to the number of students entering graduateschool,and as the GRE scores show, graduate-school-bound math-ematics students will quite likely fare well in head-to-headcompetition with other students. The crucial missing ingre-dient is faculty encouragement.A similar problem of weak proposal pressure exists in theCSIP program, although almost certainly for different rea-

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Keane Leads US Olympiad Team To 1st Place Tie With USSR

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