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1998 AIME Problems/Problem 2
== Problem == [[Image:AIME_1998-2.png|thumb|300px|right]]

6 KB (913 words) - 16:34, 6 August 2020
1998 AHSME Problems/Problem 2
== Problem 2 == ...and <math>D</math> represent four different digits selected from <math>0,1,2,\ldots ,9.</math> If <math>(A+B)/(C+D)</math> is an integer that is as larg

1,008 bytes (167 words) - 14:28, 5 July 2013
1998 AJHSME Problems/Problem 2
== Problem == ...{c}</math>, what is the value of <math>\begin{tabular}{r|l}3&4 \\ \hline 1&2\end{tabular}</math>?

797 bytes (126 words) - 15:40, 20 October 2016
1998 USAMO Problems/Problem 2
== Problem == C1=circle(O,2);

4 KB (656 words) - 17:26, 20 June 2019
1998 IMO Problems/Problem 2
==Problem== contestants. Prove that k/a ≥ (b − 1)/(2b).

451 bytes (79 words) - 23:47, 18 November 2023
1998 JBMO Problems/Problem 2
==Problem 2== <math>\cos X = \frac{AC ^ {2} + AD ^ {2} - DC ^ {2}}{ 2 \cdot AC \cdot AD }</math>

3 KB (554 words) - 08:31, 2 July 2020
1998 CEMC Gauss (Grade 7) Problems/Problem 2
== Problem == == Solution 2==

651 bytes (98 words) - 16:14, 15 June 2022
1998 APMO Problems/Problem 2
== Problem == ...<math>b</math>, <math>(36a + b)(36b + a)</math> cannot be a power of <math>2</math>.

2 KB (297 words) - 12:50, 22 July 2021
1998 OIM Problems/Problem 2
== Problem ==

564 bytes (96 words) - 15:39, 13 December 2023

Page text matches

MATHCOUNTS
...cluding Art of Problem Solving, the focus of MATHCOUNTS is on mathematical problem solving. Students are eligible for up to three years, but cannot compete be ...er), 2-2.5 (State/National) Target: 1.5 (School), 2 (Chapter), 2-2.5 (State/National)}}

10 KB (1,497 words) - 11:42, 10 March 2024
American Invitational Mathematics Examination
...ministered by the [[Mathematical Association of America]] (MAA). [[Art of Problem Solving]] (AoPS) is a proud sponsor of the AMC! ...blem 1-5: 3 Problem 6-10: 4 Problem 10-12: 5 Problem 12-15: 6}}

8 KB (1,057 words) - 12:02, 25 February 2024
Constructive counting
This is a problem where constructive counting is not the simplest way to proceed. This next e === Example 2 ===

12 KB (1,896 words) - 23:55, 27 December 2023
Fibonacci sequence
...m is the sum of the two preceding it. The first few terms are <math>1, 1, 2, 3, 5, 8, 13, 21, 34, 55,...</math>. ...ion|recursively]] as <math>F_1 = F_2 = 1</math> and <math>F_n=F_{n-1}+F_{n-2}</math> for <math>n \geq 3</math>. This is the simplest nontrivial example

6 KB (957 words) - 23:49, 7 March 2024
Complex number
...mplex numbers''' arise when we try to solve [[equation]]s such as <math> x^2 = -1 </math>. ...from this addition, we are not only able to find the solutions of <math> x^2 = -1 </math> but we can now find ''all'' solutions to ''every'' polynomial.

5 KB (860 words) - 15:36, 10 December 2023
AIME Problems and Solutions
...in the AoPSWiki, please consider adding them. Also, if you notice that a problem in the Wiki differs from the original wording, feel free to correct it. Fi | colspan="2"| [[1999 AIME | AIME]]

3 KB (391 words) - 16:00, 21 February 2024
Olimpiada de Mayo/1997
...contains the full set of test problems. The rest contain each individual problem and its solution. * [[1997 I Problems/Problem 1|Problem 1]]

856 bytes (98 words) - 14:53, 3 July 2009
1999 AIME
...contains the full set of test problems. The rest contain each individual problem and its solution. * [[1999 AIME Problems/Problem 1|Problem 1]]

1 KB (118 words) - 08:41, 7 September 2011
1998 AIME
...contains the full set of test problems. The rest contain each individual problem and its solution. * [[1998 AIME Problems]]

1 KB (114 words) - 08:39, 7 September 2011
1997 AIME
...contains the full set of test problems. The rest contain each individual problem and its solution. * [[1997 AIME Problems/Problem 1|Problem 1]]

1 KB (114 words) - 08:39, 7 September 2011
1997 AIME Problems
== Problem 1 == [[1997 AIME Problems/Problem 1|Solution]]

7 KB (1,098 words) - 17:08, 25 June 2020
1998 AIME Problems
{{AIME Problems|year=1998}} == Problem 1 ==

7 KB (1,084 words) - 02:01, 28 November 2023
1999 AIME Problems
== Problem 1 == [[1999 AIME Problems/Problem 1|Solution]]

7 KB (1,094 words) - 13:39, 16 August 2020
1985 AIME Problems/Problem 5
== Problem == ..., a_2, a_3, \ldots</math> is chosen so that <math>a_n = a_{n - 1} - a_{n - 2}</math> for each <math>n \ge 3</math>. What is the sum of the first 2001 te

2 KB (410 words) - 13:37, 1 May 2022
1998 AIME Problems/Problem 15
== Problem == ...have to leave the vertex, so every vertex reached is equivalent to adding 2 more segments. So the degree of each vertex must be even, with the exceptio

9 KB (1,671 words) - 22:10, 15 March 2024
1998 AIME Problems/Problem 14
== Problem == ...angular box has half the volume of an <math>(m + 2)\times(n + 2)\times(p + 2)</math> rectangular box, where <math>m, n,</math> and <math>p</math> are in

2 KB (390 words) - 21:05, 29 May 2023
1998 AIME Problems/Problem 13
== Problem == ...the sum of the complex power sums of all nonempty [[subset]]s of <math>\{1,2,\ldots,n\}.</math> Given that <math>S_8 = - 176 - 64i</math> and <math> S_

2 KB (384 words) - 19:02, 20 October 2023
1998 AIME Problems/Problem 12
== Problem == ...ivisible by the square of any [[prime]]. What is <math>a^{2} + b^{2} + c^{2}</math>?

5 KB (876 words) - 20:27, 9 June 2022
1998 AIME Problems/Problem 11
== Problem == ...that it is of the same length of a face diagonal, making it <math>20\sqrt{2}</math>.

7 KB (1,084 words) - 11:48, 13 August 2023
1998 AIME Problems/Problem 10
== Problem == <cmath>x^2 + (r-100)^2 = (r+100)^2 \Longrightarrow x = 20\sqrt{r}</cmath>

3 KB (496 words) - 13:02, 5 August 2019
1998 AIME Problems/Problem 9
== Problem == label(rotate(45)*"$M_1-M_2\le m$",((m+60)/2,(60-m)/2),NW,fontsize(9));

4 KB (624 words) - 18:34, 18 February 2018
1998 AIME Problems/Problem 8
== Problem == | 0 || 1 || 2 || 3 || 4 || 5 || 6

2 KB (354 words) - 19:37, 24 September 2023
1998 AIME Problems/Problem 7
== Problem == Note that this is an algebraic bijection, we have simplified the problem and essentially removed the odd condition, so now we can finish with plain

5 KB (684 words) - 11:41, 13 August 2023
1998 AIME Problems/Problem 6
== Problem == <math>0 = RC^2 - 112\cdot847</math>

2 KB (254 words) - 19:38, 4 July 2013
1998 AIME Problems/Problem 5
== Problem == Given that <math>A_k = \frac {k(k - 1)}2\cos\frac {k(k - 1)\pi}2,</math> find <math>|A_{19} + A_{20} + \cdots + A_{98}|.</math>

1 KB (225 words) - 02:20, 16 September 2017
1998 AIME Problems/Problem 4
== Problem == Nine tiles are numbered <math>1, 2, 3, \cdots, 9,</math> respectively. Each of three players randomly selects

5 KB (917 words) - 02:37, 12 December 2022
1998 AIME Problems/Problem 3
== Problem == The graph of <math> y^2 + 2xy + 40|x|= 400</math> partitions the plane into several regions. What

1 KB (198 words) - 20:13, 23 February 2018
1998 AIME Problems/Problem 2
== Problem == [[Image:AIME_1998-2.png|thumb|300px|right]]

6 KB (913 words) - 16:34, 6 August 2020
1998 AIME Problems/Problem 1
== Problem == ...<math>k</math> has only 2s and 3s in its prime factorization, or <math>k = 2^a3^b</math>.

2 KB (289 words) - 22:50, 23 April 2024
2000 AIME I Problems/Problem 3
== Problem == ...e [[relatively prime]] positive integers, the [[coefficient]]s of <math>x^{2}</math> and <math>x^{3}</math> are equal. Find <math>a + b</math>.

679 bytes (98 words) - 00:51, 2 November 2023
2000 AIME II Problems/Problem 14
== Problem == ...on <math>(f_1,f_2,f_3,\ldots,f_m)</math>, meaning that <math>k=1!\cdot f_1+2!\cdot f_2+3!\cdot f_3+\cdots+m!\cdot f_m</math>, where each <math>f_i</math

7 KB (1,131 words) - 14:49, 6 April 2023
IMO Problems and Solutions
* [[1959 IMO Problems/Problem 1 | Problem 1]] proposed by Poland * [[1959 IMO Problems/Problem 2 | Problem 2]] proposed by Constantin Ionescu-Tiu, Romania

35 KB (4,009 words) - 20:25, 21 February 2024
Balkan Mathematical Olympiad
...u>Problem 1: 6 Problem 2: 6.5 Problem 3: 7.5 Problem 4: 8}} *In every competition or test there are four problem usually covering [[geometry]], [[number theory]], [[algebra]], and [[combin

4 KB (578 words) - 00:12, 29 August 2018
Junior Balkan Mathematical Olympiad
...ficulty=4 - 6|breakdown=Problem 1: 4 Problem 2/3: 5 Problem 4: 6}} *In every competition or test there are four problem usually covering [[geometry]], [[number theory]], [[algebra]], and [[combin

3 KB (472 words) - 18:49, 2 February 2019
JBMO Problems and Solutions, with authors
* [[1997 JBMO Problems/Problem 1 | Problem 1]] proposed by Bulgaria * [[1997 JBMO Problems/Problem 2 | Problem 2]] proposed by Cyprus

6 KB (524 words) - 17:17, 17 August 2018
Balkan MO Problems and Solutions, with authors
* [[1984 BMO Problems/Problem 1 | Problem 1]] * [[1984 BMO Problems/Problem 2 | Problem 2]]

4 KB (371 words) - 16:41, 1 January 2024
2007 AMC 12A Problems/Problem 22
...ate|[[2007 AMC 12A Problems|2007 AMC 12A #22]] and [[2007 AMC 10A Problems/Problem 25|2007 AMC 10A #25]]}} == Problem ==

15 KB (2,558 words) - 19:33, 4 February 2024
1998 PMWC Problems
== Problem I1 == Calculate: <math>\frac{1*2*3+2*4*6+3*6*9+4*8*12+5*10*15}{1*3*5+2*6*10+3*9*15+4*12*20+5*15*25}</math>

11 KB (1,738 words) - 19:25, 10 March 2015
1997 PMWC Problems/Problem T3
==Problem== ...0 thousands and multiply it by 2 and subtract 5, since we are leaving out 1998 and 1999.

1 KB (202 words) - 14:39, 20 April 2014
1999 AHSME Problems
== Problem 1 == <math>1 - 2 + 3 -4 + \cdots - 98 + 99 = </math>

13 KB (1,945 words) - 18:28, 19 June 2023
1999 USAMO
...contains the full set of test problems. The rest contain each individual problem and its solution. ** [[1999 USAMO Problems/Problem 1 | Problem 1]]

808 bytes (95 words) - 15:27, 29 April 2020
1998 AHSME Problems/Problem 24
== Problem == ...that each <math>d_i</math> can be any of the ten decimal digits <math>0,1,2, \ldots, 9</math>, the number of different memorable telephone numbers is

2 KB (330 words) - 10:14, 10 August 2016
1998 AHSME Problems/Problem 22
== Problem == \qquad\mathrm{(D)}\ 2

1 KB (138 words) - 10:41, 22 April 2016
1998 AHSME Problems/Problem 17
== Problem == : (b) <math>f(0) = 2</math>.

656 bytes (94 words) - 22:16, 28 March 2024
1998 AHSME Problems/Problem 26
== Problem == pair D=(0,0), C=(0,24*3^0.5), A=(46,0), E=(72,0), B=(46+13/2,13*3^.5/2);

3 KB (391 words) - 14:30, 5 July 2013
1998 AHSME Problems/Problem 27
== Problem == [[Image:1998 AHSME num. 27.png]]

3 KB (403 words) - 23:00, 10 August 2020
APMO Problems and Solutions
** [[1989 APMO Problems/Problem 1 | Problem 1]] ** [[1989 APMO Problems/Problem 2 | Problem 2]]

7 KB (626 words) - 21:52, 19 August 2023
1998 APMO
...contains the full set of test problems. The rest contain each individual problem and its solution. * [[1998 APMO Problems|Problems]]

549 bytes (60 words) - 09:45, 30 May 2012
1999 AHSME
...contains the full set of test problems. The rest contain each individual problem and its solution. ** [[1999 AHSME Problems/Problem 1|Problem 1]]

2 KB (178 words) - 13:28, 20 February 2020
1998 AHSME Problems
|year = 1998 == Problem 1 ==

15 KB (2,222 words) - 10:40, 11 August 2020
1998 AHSME Problems/Problem 28
== Problem == ...t angle <math>CAD</math> is twice angle <math>DAB</math>. If <math>AC/AD = 2/3</math>, then <math>CD/BD = m/n</math>, where <math>m</math> and <math>n</

4 KB (662 words) - 00:51, 3 October 2023
1998 AHSME Problems/Problem 8
== Problem == ...8,1),N); MP("I",(.17/2,.25),(0,0));MP("I",(.17/2,.75),(0,0));MP("I",(1-.17/2,.75),(0,0));MP("II",(.5-.17,.4),(0,0));MP("II",(.5-.17,.6),(0,0));MP("II",(

2 KB (347 words) - 11:28, 2 December 2019
1998 AHSME Problems/Problem 4
== Problem == <center><math>\left[[60,30,90],[2,1,3],[10,5,15]\right]?</math></center>

714 bytes (95 words) - 14:28, 5 July 2013
1998 AHSME
...contains the full set of test problems. The rest contain each individual problem and its solution. * [[1998 AHSME Problems|Entire Exam]]

2 KB (173 words) - 03:44, 29 September 2014
1998 AHSME Problems/Problem 12
== Problem == <math> \mathrm{(A) \ }1 \qquad \mathrm{(B) \ }2 \qquad \mathrm{(C) \ }3 \qquad \mathrm{(D) \ } 4\qquad \mathrm{(E) \ }7 </m

638 bytes (84 words) - 14:29, 5 July 2013
1998 AJHSME Problems/Problem 19
==Problem== ...)}\ \dfrac{1}{2} \qquad \text{(D)}\ \dfrac{1}{3} \qquad \text{(E)}\ \dfrac{2}{3}</math>

2 KB (242 words) - 19:53, 31 October 2016
1998 AHSME Problems/Problem 30
== Problem == ...= \min(x_n,y_n)</math>. The last non-zero digit is the last digit of <math>2^{x_n-z_n} 5^{y_n-z_n} r_n</math>.

3 KB (486 words) - 10:37, 11 August 2020
1998 AHSME Problems/Problem 25
== Problem == A piece of graph paper is folded once so that <math>(0,2)</math> is matched with <math>(4,0)</math>, and <math>(7,3)</math> is match

4 KB (722 words) - 19:47, 28 October 2022
1998 AHSME Problems/Problem 23
== Problem == The graphs of <math>x^2 + y^2 = 4 + 12x + 6y</math> and <math>x^2 + y^2 = k + 4x + 12y</math> intersect when <math>k</math> satisfies <math>a \le k

1 KB (193 words) - 09:12, 2 December 2018
1998 AHSME Problems/Problem 21
== Problem == ...{d^2}h \qquad \mathrm{(D) \ } \frac {h^2}d \qquad \mathrm{(E) \ } \frac{d^2}{h-d}</math>

1 KB (220 words) - 14:29, 5 July 2013
1998 AHSME Problems/Problem 20
== Problem == <math>\textrm{(A)}\ 2 \qquad \textrm{(B)}\ 3 \qquad \textrm{(C)}\ 4 \qquad \textrm{(D)}\ 5 \qquad

2 KB (328 words) - 16:40, 29 September 2018
1998 AHSME Problems/Problem 19
== Problem == <math> \mathrm{(A) \ }0 \qquad \mathrm{(B) \ }2 \qquad \mathrm{(C) \ }4 \qquad \mathrm{(D) \ }6 \qquad \mathrm{(E) \ } 8</m

2 KB (368 words) - 11:08, 4 February 2017
1998 AHSME Problems/Problem 18
== Problem == <math>\qquad \mathrm{(D) \ }A^2 - M^2 + C^2 = 0 \qquad \mathrm{(E) \ } 2A + 2M = 3C </math>

1 KB (187 words) - 14:29, 5 July 2013
1998 AHSME Problems/Problem 13
== Problem == We have <math>144 = 2^4 3^2</math>.

1 KB (195 words) - 14:29, 5 July 2013
1998 AHSME Problems/Problem 11
== Problem == <math> \mathrm{(A) \ }1 \qquad \mathrm{(B) \ }2 \qquad \mathrm{(C) \ }4 \qquad \mathrm{(D) \ }5 \qquad \mathrm{(E) \ }6 </m

929 bytes (132 words) - 14:29, 5 July 2013
2004 AMC 12B Problems/Problem 12
==Problem== <math> \mathrm{(A) \ } -2004 \qquad \mathrm{(B) \ } -2 \qquad \mathrm{(C) \ } 0 \qquad \mathrm{(D) \ } 4003 \qquad \mathrm{(E) \ }

2 KB (364 words) - 11:41, 13 October 2021
2002 AMC 12A Problems/Problem 21
== Problem == ...ider the sequence of numbers: <math>4,7,1,8,9,7,6,\dots</math> For <math>n>2</math>, the <math>n</math>-th term of the sequence is the units digit of th

2 KB (274 words) - 11:06, 18 July 2023
Olimpiada de Mayo
...test], [http://www.oma.org.ar/internacional/resultados_generales-may4.htm 1998 test results] ===Problem 1===

4 KB (668 words) - 14:52, 17 August 2020
1998 USAMO
...contains the full set of test problems. The rest contain each individual problem and its solution. * [[1998 USAMO Problems|Entire Test]]

773 bytes (91 words) - 18:11, 17 September 2012
1998 USAMO Problems/Problem 3
== Problem == ...cdots a_n</math> be real numbers in the interval <math>\left(0,\frac {\pi}{2}\right)</math> such that

2 KB (322 words) - 13:31, 23 August 2023
1998 AHSME Problems/Problem 5
== Problem== If <math>2^{1998}-2^{1997}-2^{1996}+2^{1995} = k \cdot 2^{1995},</math> what is the value of <math>k</math>?

878 bytes (110 words) - 14:28, 5 July 2013
1996 AJHSME Problems
==Problem 1== <math>\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 5 \qquad \text

13 KB (1,880 words) - 13:35, 19 February 2020
1997 AJHSME
...contains the full set of test problems. The rest contain each individual problem and its solution. ** [[1997 AJHSME Problems/Problem 1]]

2 KB (141 words) - 23:42, 8 October 2014
1997 AJHSME Problems
==Problem 1== [[1997 AJHSME Problems/Problem 1|Solution]]

12 KB (1,702 words) - 12:35, 6 November 2022
1998 AJHSME
...contains the full set of test problems. The rest contain each individual problem and its solution. * [[1998 AJHSME Problems|Entire Test]]

2 KB (141 words) - 23:43, 8 October 2014
1998 AJHSME Problems
|year = 1998 ==Problem 1==

14 KB (1,920 words) - 19:31, 31 January 2024
1998 USAMO Problems
Problems of the [[1998 USAMO | 1998]] [[USAMO]]. ===Problem 1===

3 KB (486 words) - 06:11, 24 November 2020
1998 USAMO Problems/Problem 1
== Problem == Suppose that the set <math>\{1,2,\cdots, 1998\}</math> has been partitioned into disjoint pairs <math>\{a_i,b_i\}</math>

1 KB (184 words) - 10:56, 30 January 2021
1999 AMC 8
...contains the full set of test problems. The rest contain each individual problem and its solution. ** [[1999 AMC 8 Problems/Problem 1|Problem 1]]

2 KB (163 words) - 00:24, 31 March 2015
1999 AMC 8 Problems
==Problem 1== <math>(6?3) + 4 - (2 - 1) = 5</math> To make this statement true, the question mark between the

17 KB (2,394 words) - 19:51, 8 May 2023
1998 AJHSME Problems/Problem 24
==Problem== draw((2,0)--(2,-.5));

5 KB (686 words) - 15:35, 29 May 2021
1998 USAMO Problems/Problem 5
==Problem== ...e is a set <math>S</math> of <math>n</math> integers such that <math>(a-b)^2</math> divides <math>ab</math> for every distinct <math>a,b\in S</math>.

1 KB (244 words) - 09:44, 20 July 2016
1998 AHSME Problems/Problem 3
== Problem 3 == <center><math>\begin{tabular}{rr}&\ \texttt{7 a 2}\\ -& \texttt{4 8 b} \\

1 KB (230 words) - 19:46, 10 March 2015
1998 AHSME Problems/Problem 6
== Problem == If <math>1998</math> is written as a product of two positive integers whose difference is

1 KB (157 words) - 14:28, 5 July 2013
1998 AHSME Problems/Problem 9
== Problem == <math>\frac{70}{2} = 35</math> people heard <math>20</math> minutes of the talk, for a total

1 KB (189 words) - 14:29, 5 July 2013
1998 AHSME Problems/Problem 1
== Problem 1 == ...<math>w = 7, x = 5, y = 4, z = 8</math>. In rectangle E, <math>w = 9, x = 2, y = 7, z = 0</math>. These five rectangles are placed, without rotating or

2 KB (346 words) - 14:28, 5 July 2013
1998 AHSME Problems/Problem 10
== Problem== ...the larger square. Thus the area of the larger square is <math>(x+y)^2=7^2=\boxed{49\text{ (A)}}</math>.

1 KB (208 words) - 14:29, 5 July 2013
1998 AHSME Problems/Problem 14
== Problem == ...positive, and one negative. If this parabola is the graph of <math>y = ax^2 + bx + c,</math> which of <math>a,b,</math> and <math>c</math> must be posi

1 KB (219 words) - 14:29, 5 July 2013
1998 AHSME Problems/Problem 15
== Problem== <math> \mathrm{(A) \ }\sqrt{3} \qquad \mathrm{(B) \ }2 \qquad \mathrm{(C) \ }\sqrt{6} \qquad \mathrm{(D) \ }3 \qquad \mathrm{(E) \

764 bytes (123 words) - 14:29, 5 July 2013
1998 AHSME Problems/Problem 16
== Problem == [[Image:Problem 16.png|center|###px]]

2 KB (307 words) - 18:58, 11 January 2014
1998 AHSME Problems/Problem 2
== Problem 2 == ...and <math>D</math> represent four different digits selected from <math>0,1,2,\ldots ,9.</math> If <math>(A+B)/(C+D)</math> is an integer that is as larg

1,008 bytes (167 words) - 14:28, 5 July 2013
1998 AHSME Problems/Problem 29
== Problem== <math> \mathrm{(A) \ } 4.0 \qquad \mathrm{(B) \ } 4.2 \qquad \mathrm{(C) \ } 4.5 \qquad \mathrm{(D) \ } 5.0 \qquad \mathrm{(E) \

907 bytes (132 words) - 00:54, 30 January 2019
1998 AJHSME Problems/Problem 1
==Problem== {{AJHSME box|year=1998|before=First question|num-a=2}}

764 bytes (106 words) - 17:27, 25 November 2022
1998 AJHSME Problems/Problem 13
==Problem== draw((1,1)--(2,0)--(4,2));

1 KB (155 words) - 00:16, 31 March 2015
1998 AJHSME Problems/Problem 2
== Problem == ...{c}</math>, what is the value of <math>\begin{tabular}{r|l}3&4 \\ \hline 1&2\end{tabular}</math>?

797 bytes (126 words) - 15:40, 20 October 2016
1998 AJHSME Problems/Problem 12
==Problem== <math>2\left(1-\dfrac{1}{2}\right) + 3\left(1-\dfrac{1}{3}\right) + 4\left(1-\dfrac{1}{4}\right) + \cd

1 KB (157 words) - 11:48, 20 December 2018
1998 AJHSME Problems/Problem 3
==Problem== <math>\text{(A)}\ 1 \qquad \text{(B)} \dfrac{25}{16} \qquad \text{(C)}\ 2 \qquad \text{(D)}\ \dfrac{43}{20} \qquad \text{(E)}\ \dfrac{47}{16}</math>

590 bytes (62 words) - 00:09, 31 March 2015
1998 AJHSME Problems/Problem 5
==Problem== ==Solution 2==

1 KB (153 words) - 22:10, 13 January 2023
1998 AJHSME Problems/Problem 6
==Problem== draw((0,0)--(0,2)--(1,2)--(2,3)--(2,2)--(3,2)--(3,0)--(2,0)--(2,1)--(1,0)--cycle);

2 KB (294 words) - 17:52, 26 October 2020
1998 AJHSME Problems/Problem 7
==Problem== ...ext{(C)}\ (199.8)^2 \qquad \text{(D)}\ (1998)^2 \qquad \text{(E)}\ (19980)^2</math>

508 bytes (51 words) - 00:28, 5 July 2013
1998 AJHSME Problems/Problem 9
==Problem== <math>\text{(A)}\ 2.00\text{ dollars} \qquad \text{(B)}\ 3.75\text{ dollars} \qquad \text{(C)}\

967 bytes (125 words) - 19:49, 6 August 2020
1998 AJHSME Problems/Problem 11
==Problem== <math>S = 3-1=2 </math>

708 bytes (101 words) - 00:29, 5 July 2013
1998 AJHSME Problems/Problem 10
==Problem== ...<math>\text{Z}</math> represents a different integer in the set <math>\{ 1,2,3,4\}</math>, but not necessarily in that order. If <math>\dfrac{\text{W}}

1 KB (212 words) - 00:29, 5 July 2013
1998 AJHSME Problems/Problem 15
In the very center of the Irenic Sea lie the beautiful Nisos Isles. In 1998 the number of people on these islands is only 200, but the population tripl ==Problem 15==

1 KB (173 words) - 20:55, 11 May 2021
1998 AJHSME Problems/Problem 16
In the very center of the Irenic Sea lie the beautiful Nisos Isles. In 1998 the number of people on these islands is only 200, but the population tripl ==Problem 16==

1 KB (206 words) - 17:52, 17 April 2021
1998 AJHSME Problems/Problem 17
In the very center of the Irenic Sea lie the beautiful Nisos Isles. In 1998 the number of people on these islands is only 200, but the population tripl ==Problem 17==

2 KB (354 words) - 14:30, 29 May 2021
1998 AJHSME Problems/Problem 18
==Problem== draw((2,0)--(2,1)--(4,1)--(4,0)--cycle);

2 KB (278 words) - 17:21, 20 February 2020
1998 AJHSME Problems/Problem 20
==Problem== ...21.95</math> per square yard and the padding to put under it costs <math>\$2.55</math> per square yard. Felix plans to install padding and carpet in the

1 KB (160 words) - 01:00, 5 February 2024
1998 AJHSME Problems/Problem 21
==Problem== ===Solution 2===

2 KB (410 words) - 18:55, 8 February 2023
1998 AJHSME Problems/Problem 22
==Problem== Rule 2: If the integer is even and greater than 9, divide it by 2.

1 KB (191 words) - 00:32, 5 July 2013
1998 AJHSME Problems/Problem 25
==Problem== ...at the beginning, then after Amy doubles his money, he has <math>36 \times 2 = 72</math> dollars after the first step.

1 KB (216 words) - 13:56, 18 August 2019
1998 AJHSME Problems/Problem 23
==Problem== which is the pattern of "triangular numbers". Each time, the number <math>1, 2, 3, 4, 5...</math> is added to the previous term. Thus, the first eight te

2 KB (279 words) - 15:23, 29 May 2021
1997 USAMO
...contains the full set of test problems. The rest contain each individual problem and its solution. ** [[1997 USAMO Problems/Problem 1|Problem 1]]

656 bytes (69 words) - 18:11, 17 September 2012
1997 USAMO Problems
=== Problem 1 === [[1997 USAMO Problems/Problem 1|Solution]]

3 KB (507 words) - 14:31, 12 April 2023
1996 AJHSME Problems/Problem 13
==Problem== ...p day. The organizers of the event expect that in each of the years 1997, 1998, and 1999, participation will increase by 50% over the previous year. The

1 KB (193 words) - 00:24, 5 July 2013
1997 AHSME
...contains the full set of test problems. The rest contain each individual problem and its solution. * [[1997 AHSME Problems/Problem 1|Problem 1]]

2 KB (174 words) - 00:30, 2 October 2014
1997 AHSME Problems
== Problem 1 == <math> \begin{array}{ccc}& 2 & a\\ \times & b & 3\\ \hline & 6 & 9\\ 9 & 2\\ \hline 9 & 8 & 9\end{array} </math>

17 KB (2,590 words) - 13:38, 19 February 2020
1998 USAMO Problems/Problem 2
== Problem == C1=circle(O,2);

4 KB (656 words) - 17:26, 20 June 2019
1997 IMO
...k contains the full set of test problems. The rest contain each individual problem and its solution. **[[1997 IMO Problems/Problem 1 | Problem 1]]

648 bytes (73 words) - 17:11, 30 December 2019
1998 IMO
...k contains the full set of test problems. The rest contain each individual problem and its solution. *[[1998 IMO Problems|Entire Test]]

645 bytes (73 words) - 17:10, 30 December 2019
1999 IMO
...k contains the full set of test problems. The rest contain each individual problem and its solution. **[[1999 IMO Problems/Problem 1 | Problem 1]]

646 bytes (73 words) - 17:10, 30 December 2019
1998 USAMO Problems/Problem 6
== Problem == ...which exactly <math>k</math> of the quadrilaterals <math>A_{i}A_{i+1}A_{i+2}A_{i+3}</math> have an inscribed circle. (Here <math>A_{n+j} = A_{j}</math>

5 KB (871 words) - 18:59, 10 May 2023
1999 USAMO Problems
===Problem 1=== Prove that at least <math>(n^{2}-2)/3</math> checkers have been placed on the board.

3 KB (465 words) - 13:35, 4 July 2013
1999 CEMC Gauss (Grade 7)
...contains the full set of test problems. The rest contain each individual problem and its solution. * [[1999 CEMC Gauss (Grade 7) Problems/Problem 1]]

2 KB (179 words) - 00:16, 26 October 2014
1998 CEMC Gauss (Grade 7)
...contains the full set of test problems. The rest contain each individual problem and its solution. * [[1998 CEMC Gauss (Grade 7) Answer Key]]

2 KB (181 words) - 00:17, 26 October 2014
1998 CEMC Gauss (Grade 7) Problems
...ing, consult the pdf: https://www.cemc.uwaterloo.ca/contests/past_contests/1998/1998Gauss7Contest.pdf == Problem 1 ==

10 KB (1,590 words) - 16:43, 29 January 2021
1999 CEMC Gauss (Grade 7) Problems
== Problem 1 == [[1998 CEMC Gauss (Grade 7) Problems/Problem 1|Solution]]

5 KB (621 words) - 00:50, 26 October 2014
1998 IMO Problems/Problem 1
==Problem== {{IMO box|year=1998|before=First Question|num-a=2}}

585 bytes (94 words) - 23:53, 18 November 2023
1998 IMO Problems/Problem 2
==Problem== contestants. Prove that k/a ≥ (b − 1)/(2b).

451 bytes (79 words) - 23:47, 18 November 2023
1998 IMO Problems/Problem 3
===Problem=== <math>d(n^2)/d(n) = k</math> for some <math>n</math>.

3 KB (566 words) - 23:48, 18 November 2023
1998 IMO Problems/Problem 6
==Problem== Determine the least possible value of <math>f(1998),</math> where <math>f:\Bbb{N}\to \Bbb{N}</math> is a function such that fo

417 bytes (65 words) - 23:54, 18 November 2023
1997 JBMO Problems
==Problem 1== [[1997 JBMO Problems/Problem 1#Solution|Solution]]

2 KB (245 words) - 22:44, 14 September 2023
1997 JBMO
* [[1997 JBMO Problems/Problem 1 | Problem 1]] * [[1997 JBMO Problems/Problem 2 | Problem 2]]

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1997 JBMO Problems/Problem 5
== Problem == ...integers such that <cmath> n_1^2 + n_2^2 + \cdots + n_{1997}^2 = n_{1998}^2. </cmath> Show that at least two of the numbers are even.

2 KB (293 words) - 21:12, 7 August 2018
1998 JBMO Problems
==Problem 1== ...\underbrace{22\ldots 22}_{1998}5</math> (which has 1997 of 1-s and 1998 of 2-s) is a perfect square.

933 bytes (131 words) - 20:10, 31 October 2020
1998 JBMO
...JBMO''' problems and solutions. The 2nd JBMO was held in Athens, Greece in 1998. * [[1998 JBMO Problems]]

552 bytes (57 words) - 20:50, 14 August 2018
1998 JBMO Problems/Problem 1
==Problem== ...\underbrace{22\ldots 22}_{1998}5</math> (which has 1997 of 1-s and 1998 of 2-s) is a perfect square.

1 KB (134 words) - 22:37, 14 August 2018
1999 JBMO
** [[1999 JBMO Problems/Problem 1 | Problem 1]] ** [[1999 JBMO Problems/Problem 2 | Problem 2]]

555 bytes (57 words) - 16:47, 18 August 2018
1999 JBMO Problems
==Problem 1== [[1999 JBMO Problems/Problem 1|Solution]]

2 KB (271 words) - 13:13, 25 August 2018
1998 JBMO Problems/Problem 2
==Problem 2== <math>\cos X = \frac{AC ^ {2} + AD ^ {2} - DC ^ {2}}{ 2 \cdot AC \cdot AD }</math>

3 KB (554 words) - 08:31, 2 July 2020
1998 CEMC Gauss (Grade 7) Problems/Problem 18
== Problem == The letters of the word ‘GAUSS’ and the digits in the number ‘1998’ are each cycled separately and then numbered as shown:

698 bytes (103 words) - 16:36, 29 January 2021
Know the Facts: Gmaas
- 1960 - 1998: Survey and mapping of Gmaas's 314,159,265 catfish lives. ...ntly, Leibniz had Gmaas_number 1 while Schrodinger had Gmaas_number number 2, where a lower Gmaas number indicates a higher power. (When Gmaas found out

88 KB (14,928 words) - 13:54, 29 April 2024
OIM Problems and Solutions
* [[1985 OIM Problems/Problem 1 | Problem 1]] * [[1985 OIM Problems/Problem 2 | Problem 2]]

14 KB (1,323 words) - 12:18, 13 December 2023
1998 OIM Problems/Problem 6
== Problem == Let <math>\lambda</math> be the positive root of the equation <math>t^2 - 1998t - 1 = 0</math>. The sequence <math>x_0, x_1, x_2, \cdots , x_n, \cd

720 bytes (117 words) - 15:57, 13 December 2023
XIII Olimpiada Iberoamericana de Matemáticas (OIM)
...beroamericana de Matemáticas]] was held in Puerto Plata, R. Dominicana , 1998 * [[1998 OIM Problems/Problem 1 | Problem 1]]

469 bytes (45 words) - 17:54, 14 December 2023
2002 AMC 12P Problems/Problem 14
== Problem == Find <math>i + 2i^2 +3i^3 + ... + 2002i^{2002}.</math>

2 KB (313 words) - 20:07, 10 March 2024

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