## Jul 13, 2011

1. [PDF]

### Problems, May 2011

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Problems, May 2011. Problem 1. Given six points in the interior of a circle of radius 1, show that the distance between two of these points is less than 1. ...
2. [PDF]

### Mayhem Problems

send your solutions to the problems in this edition by 1 October 2002. Solutions ... Starting this issue, problems will be printed in English and French. ...
3. [PDF]

### Problems, April 2011

www.pims.math.ca/education/math_problems/prob-4-11.pdf
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Problems, April 2011. Problem 1. If A, B, C, D, and E are any 5 points in the plane, no 3 of which lie on a line, let m(A, B, C, D, E) be the measure (in ...
4. [PDF]

### Problems, February 2011

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Problems, February 2011. Problem 1. The distances from a point inside a square to 3 consec- utive vertices of the square are 9, 10, and 7 as shown. ...
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### Problems, March 2011

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Problems, March 2011. Problem 1. Is there a perfect cube the sum of whose digits is 2011? Problem 2. The outer circle in the picture has radius a, the inner ...
6. [PDF]

### SOME PROBLEMS ON COMBINATIONAL LOGICAL CIRCUITS by Ion Mihail ...

emis.math.ca/journals/AUA/acta4/SOMENEWPR3.pdf
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by IM Nichita - Related articles
equation, and show that the problems presented in this paper are related to it. ... 3, we give a set of problems. For some of them we give solutions. ...
7. [PDF]

### Problems, April 2006

www.pims.math.ca/education/math_problems/prob-4-06.pdf
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Problems, April 2006. Problem 1. When a certain Egyptian pyramid was built, ... Problem2. A rich merchant died, and left gold coins to his children as ...
8. [PDF]

### Problems, January 2008

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Problems, January 2008. Problem 1. For any real number x, let [xj be the greatest integer... Problem 3. The figure below is a regular hexagon of area 1. ...
9. [PDF]

### Problems, March 2006

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Problems, March 2006. Problem 1. Let an = 1! + 2! + 3! + ··· + n! ... Problem 2. Alphonse and Beth ran one lap on the school 400 meter track. ...
10. [PDF]

### Solutions to October 2006 Problems

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way of settling the problem. We can, however, use a shortcut to do the counting. .....http://www.pims.math.ca/education/math problems/ ...
11. [PDF]

### ELEMENTARY PROBLEMS AND SOLUTIONS . Edited by Stanley Rabinowitz

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by S Rabinowitz - Related articles
Please send all material for ELEMENTARY PROBLEMS AND SOLUTIONS to Dr. STANLEY ... may also be sent to the problem editor by electronic mail to ...
12. [PDF]

### SOLUTIONS FOR 2011 APMO PROBLEMS Problem 1. Solution: Suppose all ...

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SOLUTIONS FOR 2011 APMO PROBLEMS. Problem 1. Solution: Suppose all of the 3 numbers a2 + b + c, b2 + c + a and c2 + a + b are perfect squares. ...
13. [PDF]

### 2011 APMO PROBLEMS Time allowed: 4 hours Each problem is worth 7 ...

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*The contest problems are to be kept confidential until they are posted on the offi ...disclose nor discuss the problems over the internet until that date. ...
14. [PDF]

### ROUTINES IN NON-ROUTINE PROBLEM SOLVING PROCESSES

emis.math.ca/proceedings/PME28/RR/RR126_Schloeglmann.pdf
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by W Schloeglmann - 2004 - Cited by 3 - Related articles
Nonroutine problem-solving, too, involves elements of routine. ... problem, I found that all nonroutine problem-solving processes utilise routines as ...
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### ELEMENTARY PROBLEMS AND SOLUTIONS

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Send all communications regarding Elementary Problems and Solutions ... Each problemor solu- tion should be submitted in legible form, preferably typed in ...
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### ADVANCED PROBLEMS AND SOLUTIONS Z ?P^W^-2*(y) = ^ ^ ( ^ / ^ (i)

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Please send all communications concerning ADVANCED PROBLEMS AND SOLUTIONS ...This department especially welcomes problems believed to be new or ...
17. ### Send all communications regarding Elementary Problems and ...

to existing problems will be welcomed. The proposer should submit each problem with solution in legible form, preferably typed in double ...
18. [PDF]

### MULTIPLE SOLUTIONS FOR NONLINEAR DISCONTINUOUS STRONGLY RESONANT ...

emis.math.ca/journals/HOA/AAA/Volume5_2/135.pdf
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by NC KOUROGENIS - 2000 - Related articles
We consider quasilinear strongly resonant problems with discontinuous right-hand side. To develop an existence theory we pass to a multivalued problem by, ...
19. [PDF]

### ELEMENTARY PROBLEMS AND SOLUTIONS Edited by Russ Euler and Jawad Sadek

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by R Euler - Related articles
Please submit all new problem proposals and corresponding solutions to the ProblemsEditor ... Each problem and solution should be typed on separate sheets. ...
20. [PDF]

### ON f-GENERALIZED FIBONACCI SEQUENCES AND HAUSDORFF MOMENT PROBLEMS ...

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by M Rachidi - Related articles
problem associated with Y consists of finding a positive Borel measure /i such that ... If this problem has a solution JH , we say that ju is the repre- ...
21. [PDF]

### ELEMENTARY PROBLEMS AND SOLUTIONS Edited by Stanley Rabinowitz

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by S Rabinowitz - Related articles
Please send all material for ELEMENTARY PROBLEMS AND SOLUTIONS to Dr. STANLEY ... may also be sent to the problem editor by electronic mail to ...
22. [PDF]

### 215 She Does Math! real-life problems from women on the job ...

215. BOOK REVIEWS. Edited by ANDY LIU. She Does Math! real-life problems from women on the job, edited by. Marla Parker. ...
23. [PDF]

### CONVERGENCE ANALYSIS OF THE ITERATIVE METHODS FOR QUASI ...

emis.math.ca/journals/HOA/IJMMS/Volume11_2/183086.pdf
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by MA NOOR - 1988 - Cited by 5 - Related articles
Quasi complementarity problem, quasi variational inqualitv, ... many seemingly tmrelated free boundary value problems arising in fluid flow through ...
24. [PDF]

### ELEMENTARY PROBLEMS AND SOLUTIONS n\ dtn \ - t - t* 85

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Please send all material for ELEMENTARY PROBLEMS AND SOLUTIONS to ...Correspondence may also he sent to the problem editor by electronic ...
25. [PDF]

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Please send all communications concerning ADVANCED PROBLEMS AND SOLUTIONS ...This department especially welcomes problems believed to be new or ...
26. [PDF]

### ELEMENTARY PROBLEMS AND SOLUTIONS Edited by Muss Euler and Jawad Sadek

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Please submit all new problem proposals and corresponding solutions to the ... Solutions toproblems in this issue must be received by November 15, 2001. ...
27. [PDF]

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The problems H-350 and H-372, proposed by myself and mentioned by ... of gcd sequence given in the statement of the problem, which requires / to be ...
28. [PDF]

### THE FORMULATION OF SECOND-ORDER BOUNDARY VALUEPROBLEMS ON TIME SCALES

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by FA DAVIDSON - 2006 - Cited by 7 - Related articles
difficulties with the formulation of the problem as usually used in the literature ... and give some simple examples to highlight various problems with this ...
29. [PDF]

### ELEMENTARY PROBLEMS AND SOLUTIONS Edited by Russ Euler and Jawad Sadek

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by R Euler - Related articles
Please submit all new problem proposals and corresponding solutions to the Problems Edi-... Each problem and solution should be typed on separate sheets. ...
30. [PDF]

### ELEMENTARY PROBLEMS AND SOLUTIONS Edited by Stanley Rabinowitz ...

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by S Rabinowitz - Related articles
Please send all material for ELEMENTARY PROBLEMS AND SOLUTIONS to ... received within six months of publication of the problem. Solutions typed in ...
31. [PDF]

### ADVANCED PROBLEMS AND SOLUTIONS Edited by Florian Luca

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by F Luca
Please send all communications concerning ADVANCED PROBLEMS AND SOLU-. TIONS to FLORIAN LUCA, ... This department especially welcomes problems believed to ...
32. [PDF]

### Characterization of the stability set for non-differentiable fuzzy ...

emis.math.ca/journals/HOA/IJMMS/Volume2005_12/890347.pdf
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by MABDELH KASSEM - 2005 - Related articles
the stability of multiobjective nonlinear programming problems with fuzzy ... kind for theseproblems, also introduced a method for decomposing the fuzzy ...
33. [PDF]

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Please send all communications concerning ADVANCED PROBLEMS AND SOLUTIONS..... For complete details of this very interesting problem, see pages 283-84 of ...
34. [PDF]

### ELEMENTARY PROBLEMS AND SOLUTIONS Edited by

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Please send all material for ELEMENTARY PROBLEMS AND SOLUTIONS to Dr. STANLEY ... may also be sent to the problem editor by electronic mail to ...
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### ELEMENTARY PROBLEMS AND SOLUTIONS « k= £ (2 r\l - W 2k=E(r) r •

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by AP HILLMAN - Cited by 3 - Related articles
ELEMENTARY PROBLEMS AND SOLUTIONS. Edited by. A. P. HILLMAN. University of New Mexico, Albuquerque, New Mexico. Send all communications regarding Elementary ...
36. ### Solutions to March 2007 Problems

Problem 1. Show how to divide any triangle T into 2007 triangles similar to ... tricks can be useful, specially in problems manufactured by tricky people. ...
37. [PDF]

### Problems, March 2008

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Problems, March 2008. Problem 1. Find integers a, b, c, d, and n such that ... Problem 3. A collection of 6 different integers is chosen at random from ...
38. [PDF]

### Problems, April 2009

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Problems, April 2009. Problem 1. The National Basketball Association (NBA) has 30 ...Problem 2. Outward facing squares are erected on the three sides of an ...
39. [PDF]

### Problems, April 2008

www.pims.math.ca/education/math_problems/prob-4-08.pdf
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Problems, April 2008. Problem 1. Let Q be the convex quadrilateral whose ... Problem 4. Show that the sum of any number of consecutive perfect cubes ...
40. [PDF]

### ELEMENTARY PROBLEMS AND SOLUTIONS Edited hy Stanley Rablnowitz

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by S Rablnowitz - Related articles
Please send all material for ELEMENTARY PROBLEMS AND SOL UTIONS to Dr. STANLEY ... Proposers of problems should normally include solutions. BASIC FORMULAS...
41. [PDF]

### ELEMENTARY PROBLEMS AND SOLUTIONS Send all communications ...

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Albuquerque, New Mexico 87106, Each problem or solu- ... ELEMENTARY PROBLEMSAND SOLUTIONS. 439. B-216 Proposed by V. E. Hoggatt, Jr., San Jose State ...
42. [PDF]

### ELEMENTARY PROBLEMS AND SOLUTIONS Edited by Stanley Rabinowitz ...

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PROBLEMS AND SOLUTIONS to. Dr. STANLEY. RABINOWITZ;. 12 VINE BROOK RD; ...new editor, all proposers have been notified about the status of their problems ...
43. [PDF]

### ADVANCED PROBLEMS AND SOLUTIONS Edited by RAYMOND E. WHITNEY Lock ...

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welcomes problems believed to be new or extending old results. ... squares and sums of consecutive squares appeared in Problem B-495. Show that ...
44. [PDF]

### Problems, January 2011

www.pims.math.ca/education/math_problems/prob-1-11.pdf
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Problems, January 2011. Problem 1. (a) Let n be even, and let P be a regular n-sided polygon ... Problem 3. Triangle ABC is right-angled at C, CQ is an ...
45. ### Solutions to February 2006 Problems

Problem 2. On March 21, Alfonso and Beti did a science experiment on the ..... Many probability problems are difficult or impossible to solve. “exactly. ...
46. [PDF]

### Solutions to December 2005 Problems

www.pims.math.ca/education/math_problems/sol-12-05.pdf
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There is not much point to reading solutions to problems that you have not ... Problem 1. Find the solutions of the equation x2 − 123456789 x + 10 = 0, ...
47. [PDF]

### Problems, April 2007

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Problems, April 2007. Problem 1. Let f(x) = x2 + 2x − 1. ... Problem 4. One can find 100 consecutive integers none of which is prime. ...
48. [PDF]

### Problems, November 2008

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Problems, November 2008. Problem 1. Let D be the 10-element set consisting of ...Problem 3. Alphonse and Beti are mathematicians who collaborate in sep- ...
49. [PDF]

### ELEMENTARY PROBLEMS AND SOLUTIONS Edited by A. P. Hillman Please ...

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In a manner analogous to that for the previous problem, show that .... ELEMENTARYPROBLEMS AND SOLUTIONS and a2. + b2. 3Po + 1 [adding 2b2 ...
50. [PDF]

### ELEMENTARY PROBLEMS AND SOLUTIONS Send all communications ...

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ELEMENTARY PROBLEMS AND SOLUTIONS. Edited by A. P. Hillman. University of New Mexico, Albuquerque, N.M.. Send all communications regarding Elementary ...
51. [PDF]

### Problems, February 2007

www.pims.math.ca/education/math_problems/prob-2-07.pdf
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Problem 4. Find (with proof) the smallest possible value of xy + yz + xz, ...http://www.pims.math.ca/education/math problems/ ...
52. [PDF]

### ADVANCED PROBLEMS AND SOLUTIONS (a) 9ikFkPk = 3(n + D(^P„ + 1 + Fn ...

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Please send all communications concerning ADVANCED PROBLEMS AND SOLUTIONS to... Editorial Note: H-307 was listed as an unsolved problem. Howevers the solu- ...
53. [PDF]

### ELEMENTARY PROBLEMS AND SOLUTIONS

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Send all communications regarding Elementary Problems and Solutions .... Please make the following correction in the October Elementary Problems and ...
54. [PDF]

### Send all communications regarding Elementary Problems and ...

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problems believed to be new in the area of recurrent sequences as well as new approaches to existing problems. The proposer should ...
55. [PDF]

### An Iterative Algorithm for Mixed Equilibrium Problems and ...

emis.math.ca/journals/HOA/FPTA/Volume2010/564361.pdf
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by YC Liou - 2010 - Cited by 1 - Related articles
a mixed equilibrium problem and the set of a variational inclusion in a real Hilbert space. ...The mixed equilibrium problems include fixed point problems, ...
56. [PDF]

### Mayhem Problems: M407-M412

Please send your solutions to the problems in this edition by ― ÖŲ ÖÝ ūž―ž ... Eachproblem is given in English and French, the official languages of Canada ...
57. [PDF]

### ELEMENTARY PROBLEMS AND SOLUTIONS Edited by Stanley Rabinowitz

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by S Rabinowitz - Related articles
Please send all material for ELEMENTARY PROBLEMS AND SOLUTLONS to Dr. STANLEY ... may also be sent to the problem editor by electronic mail to ...
58. [PDF]

### ELEMENTARY PROBLEMS AND SOLUTIONS Edited by A. P. Hillman Please ...

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Please send all material for ELEMENTARY PROBLEMS AND SOLUTIONS to ... received within six months of publication of the problem. Solutions typed in ...
59. [PDF]

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Send all communications concerning Advanced Problems and Solutions .... Hoggatt and Lind ["The Dying Rabbit Problem,ff to appear, Fibonacci ...
60. [PDF]

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This department especially welcomes problems believed to be new or ... on separate signed sheets within two months after publication of the problems. ...
61. [PDF]

### COLLOCATION SPLINE METHODS IN SOLVING BOUNDARY VALUE PROBLEMS

emis.math.ca/journals/NSJOM/Papers/23_2/NSJOM_23_2_345_350.pdf
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by K Surla - Related articles
The spline difference schemes for the problem: -53/' + p(:n)y = f(:c),y(0) : aU,y(1) : <11, ...Let us consider the following singularly perturbed problem ...
62. [PDF]

### Problems, November 2007

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Problems, November 2007. Problem 1. It is not hard to verify with a calculator that. 53 + 13. 53 + 43. = 5+1. 5+4. ,. 673 + 413. 673 + 263 ...
63. [PDF]

### Problems, January 2009

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Problems, January 2009. Problem 1. Find all pairs (x, y) of real numbers such that x2 + xy + y2 = 8 and x − xy + y = 2. Problem 2. ...
64. [PDF]

### Problems, October 2010

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Problems, October 2010. Problem 1. Find (with proof) all primes p such that p+ 6 ...Problem 2. Consider the system of equations x + y + z = a, xy + bz = 6. ...
65. [PDF]

### Problems, February 2008

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Problems, February 2008. Problem 1. An Egyptian-style pyramid has a square b × b ...Problem 3. Show that the equation x3 + 2y3 + 4z3 = 0 has exactly one ...
66. [PDF]

### Problems, November 2006

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Problems, November 2006. Problem 1. A six-sided convex polygon is inscribed in a ...Problem 3. Suppose that f(7) = 105, and that f(n + 2) = f(n + 1) + f(n) ...
67. [PDF]

### Problems, November 2009

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Problems, November 2009. Problem 1. A triangle has sides 9, 11, and 14. ... Problem 2. The numbers 1, 2, 3, . . . , 2009 are written on index cards, one ...
68. [PDF]

### Problems, November 2010

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Problems, November 2010. Problem 1. The base of an isosceles triangle is 20, ...Problem 2. Define the sequence A0, A1, A2, and so on by A0 = A1 = 1, and ...
69. [PDF]

### Solutions to December 2009 Problems

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centers are almost always useful in problems about circles. ... Problem 3. Find all solutions in real numbers of the following system of equa- ...
70. [PDF]

### Problems, February 2010

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Problems, February 2010. Problem 1. Every point on the circumference of a ... Problem 2. The picture shows six equilateral triangles, and two triangles ...
71. [PDF]

### Problems, May 2008

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Problems, May 2008. Problem 1. Alphonse and Beti work together to separate ... Problem2. For any real number u, let [uj be the greatest integer which is ...
72. [PDF]

### Problems, April 2010

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Problems, April 2010. Problem 1. In the rectangular grid below, each point is at ...Problem 2. The picture is of a rectangle whose base is greater than its ...
73. [PDF]

### Problems, May 2007

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Problems, May 2007. Problem 1. A circle meets the parabola y = x2 at four points. ...Problem 4. (a) Points P and Q are chosen on the curve x2 + 4y2 = 1 in ...
74. [PDF]

### Solutions to May 2006 Problems

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It is better to exploit the symmetry in the problem, either by keeping the .... in very appliedproblems. For example, the fact that gravitation is ...
75. [PDF]

### Problems, May 2006

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Problems, May 2006. Problem 1. In the figure below, a parallelogram has ... Problem 5. Call a set S of positive integers multiple-rich if for any positive ...
76. [PDF]

### Problems, December 2007

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Problems, December 2007. Problem 1. Which straight lines have exactly one point in ...Problem 3. What is the largest possible common divisor of n3+1 and n2 ...
77. [PDF]

### Problems, January 2007

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Problems, January 2007. Problem 1. Find three numbers in geometric progression ...Problem 2. A tangent line to the ellipse x2 + 4y2 = 4 meets the y-axis at ...
78. [PDF]

### Problems, October 2008

www.pims.math.ca/education/math_problems/prob-10-08.pdf
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Problem 4. Find all integers n such that n + 16 is a perfect square and no ...http://www.pims.math.ca/education/math problems/ ...
79. [PDF]

### Problems, January 2006

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Problems, January 2006. Problem 1. A convex quadrilateral is split into four ... Problem 3. Find the sum of all the four-digit numbers all of whose digits ...
80. [PDF]

### Problems, March 2010

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Problems, March 2010. Problem 1. Let a be the number of digits in the decimal ...Problem 4. Among all triangles inscribed in the ellipse that has equation ...
81. [PDF]

### Problems, December 2008

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Problems, December 2008. Problem 1. In the figure below, AB = 4, BC = 3, AC = 2, ...Problem 2. Prove, using only “high school” ideas, that for any positive ...
82. [PDF]

### Problems, December 2009

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Problems, December 2009. Problem 1. Alphonse and Beth play the following game. ...Problem 3. Find all solutions in real numbers of the following system of ...
83. [PDF]

### Problems, January 2010

www.pims.math.ca/education/math_problems/prob-1-10.pdf
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Problems, January 2010. Problem 1. For what values of m are the four ... Problem 3. (a) Show that if A is a positive integer, there exist a positive integer ...
84. [PDF]

### Problems, December 2010

www.pims.math.ca/education/math_problems/prob-12-10.pdf
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Problems, December 2010. Problem 1. A square is cut up into 169 squares. ... Problem 3. Imagine tossing a fair coin over and over again, until you get three ...
85. [PDF]

### Problems, May 2010

www.pims.math.ca/education/math_problems/prob-5-10.pdf
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Problems, May 2010. Problem 1. The figure below is a rhombus whose ... Problem 2. The sequence a0, a1, a2, and so on is defined by a0 = 2 and an+1 = ...
86. [PDF]

### Problems, March 2009

www.pims.math.ca/education/math_problems/prob-3-09.pdf
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Problems, March 2009. Problem 1. In the right-angled triangle below, ... Problem 2. (Please note that the originally posted version had two typos.) ...
87. [PDF]

### Problems, October 2007

www.pims.math.ca/education/math_problems/prob-10-07.pdf
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Problems, October 2007. Problem 1. Find all real numbers x such that ... Problem 2. Outward facing squares are erected on the sides of a right- ...
88. [PDF]

### Problems, February 2009

www.pims.math.ca/education/math_problems/prob-2-09.pdf
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Problems, February 2009. Problem 1. Vertex A of an equilateral triangle lies on one ...Problem 2. We have an unlimited number of 1 gram weights, 10 gram ...
89. [PDF]

### Problems, May 2009

www.pims.math.ca/education/math_problems/prob-5-09.pdf
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Problem 2. Let n be odd. Show that if an n-gon inscribed in a circle has all its angles equal,... http://www.pims.math.ca/education/math problems/ ...
90. ### Problems, December 2006

www.pims.math.ca/education/math_problems/prob-12-06.pdf
Problems, December 2006. Problem 1. Alphonse ran in a cross-country race, ... Problem5. Find all integers n such that 2n + n2 is a perfect square, and ...
91. [PDF]

### Problems, October 2006

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Problems, October 2006. Problem 1. Find exact expressions for the real solutions of ...Problem 3. Alicia started going up the Grouse Grind trail at 4:30. ...
92. [PDF]

### Problems, March 2007

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Problems, March 2007. Problem 1. Show how to divide any triangle T into 2007 ...Problem 4. Find the maximum value taken on by 3x + 4y as (x, y) ranges ...
93. [PDF]

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Send all communications concerning Advanced Problems and ... welcomes problemsbelieved to be new or extending old results. Pro- ...
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### RAYMOND E. WHITNEY PROBLEMS PROPOSED IN THIS ISSUE

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welcomes problems believed to be new or extending old results. Proposers .....ADVANCED PROBLEMS AND SOLUTIONS l(,. 1 2 4 6\^ 1 2 , 1. 2 6 1 1 A 2 4 6\ ...
95. [PDF]

### GODFRIED TOUSSAINT, McGill University Facility Location and ...

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Facility Location and Assignment Problems with Applications to Computational Musicology. In this lecture musical rhythm is represented symbolically, ...
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### ADVANCED PROBLEMS AND SOLUTIONS 1988]

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welcomes problems believed to be new or extending old results. Proposers .....ADVANCED PROBLEMS AND SOLUTIONS. M(a + 1, 2? + 1, s) _ ...
97. [PDF]

### F ^o =F a.1 +F > Fn = o* F i = i; PROBLEMS PROPOSED IN THIS ISSUE ...

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Please send all material for ELEMENTARY PROBLEMS AND SOLUTIONS to ... received within six months of publication of the problem. Solutions typed in ...
98. [PDF]

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Please send all communications concerning ADVANCED PROBLEMS AND SOLUTIONS.... Partial Solution to Problem B: We see that if 0k = Ey=J sfij then sk_l = 1 ...
99. [PDF]

### ELEMENTARY PROBLEMS AND SOLUTIONS Edited by Russ Euler ami Jawai Sadek

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Please submit all new problem proposals and corresponding solutions to the ... Solutions toproblems in this issue must be received by November 15, 2002. ...
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### ELEMENTARY PROBLEMS AND SOLUTIONS Edited by Stanley Rabinowitz

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Please send all material for ELEMENTARY PROBLEMS AND SOLUTIONS to Dr. STANLEY ... months of publication of the problem. Solutions typed in the format used ...