| 387 |
Ten adults enter a room, remove their shoes, an...
|
Combinatorics
Probability
|
| 386 |
Ten chairs are arranged in a circle. Find the n...
|
Combinatorics
|
| 385 |
Let ![$f(x)=(x^2+3x+2)^{\cos(\pi x...
</a></td>
<td>
<span class=]() Algebra
|
| 384 |
Charles has two six-sided die. One of the die i...
|
Combinatorics
Probability
|
| 383 |
Arnold is studying the prevalence of three heal...
|
Probability
|
| 382 |
Let  Algebra
|
| 381 |
Let Combinatorics
|
| 380 |
Ana, Bob, and Cao bike at constant rates of&nbs...
|
Algebra
Geometry
|
| 379 |
Find the number of ways ![$66$]() |
Combinatorics
|
| 378 |
Zou and Chou are practicing their ![]() |
Combinatorics
Probability
|
| 377 |
For a real number ![$x$]() Algebra
|
| 376 |
Let  Algebra
Geometry
|
| 375 |
Let ![$P(x) = x^2 - 3x - 7$]() |
Algebra
|
| 374 |
While watching a show, Ayako, Billy, Carlos, Da...
|
Combinatorics
|
| 373 |
For each positive integer ![$n$]() |
Algebra
|
| 372 |
Let Algebra
Geometry
Probability
|
| 371 |
Twenty distinct points are marked on a circle a...
|
Combinatorics
|
| 370 |
Azar, Carl, Jon, and Sergey are the four player...
|
Combinatorics
Probability
|
| 369 |
A regular pentagon with area ![$\s...
</a></td>
<td>
<span class=]() Geometry
|
| 368 |
Triangle ![$ABC_0$]() |
Algebra
Geometry
|
| 367 |
There is a ![$40\%$]() |
Algebra
Probability
|
| 366 |
A teacher was leading a class of four perfectly...
|
Algebra
Combinatorics
|
| 365 |
An ant makes a sequence of moves on a cube wher...
|
Combinatorics
Probability
|
| 364 |
Let Algebra
Combinatorics
|
| 363 |
The parabola with equation ![$y = ...
</a></td>
<td>
<span class=]() Algebra
Geometry
|
| 362 |
An ant makes a sequence of moves on a cube wher...
|
Combinatorics
Probability
|
| 361 |
For positive real numbers ![$s$]() |
Algebra
Geometry
|
| 360 |
Find the number of permutations ![...
</a></td>
<td>
<span class=]() Algebra
Combinatorics
|
| 359 |
Equilateral triangle ![$ABC$]() |
Algebra
Geometry
|
| 358 |
Find the arithmetic mean of all the three-digit...
|
Algebra
|
| 357 |
In a table tennis tournament, every participant...
|
Algebra
Combinatorics
|
| 356 |
For Algebra
|
| 355 |
There are ![$8!= 40320$]() Algebra
Combinatorics
|
| 354 |
The Combinatorics
|
| 353 |
A pair of fair ![$6$]() |
Combinatorics
Probability
|
| 352 |
How many of the first ten numbers of the sequen...
|
Algebra
Combinatorics
|
| 351 |
When Algebra
Combinatorics
|
| 350 |
Each of  |
Combinatorics
Probability
|
| 349 |
In the state of Coinland, coins have values&nbs...
|
Algebra
Combinatorics
|
| 348 |
The roots of ![$x...
</a></td>
<td>
<span class=]() Algebra
|
| 347 |
On top of a rectangular card with sides of leng...
|
Algebra
Geometry
|
| 346 |
A set of  Combinatorics
Probability
|
| 345 |
The numbers, in order, of each...
|
Algebra
|
| 344 |
In ![$\Delta ABC$]() |
Algebra
Geometry
|
| 343 |
Each face of two noncongruent parallelepipeds i...
|
Algebra
Geometry
|
| 342 |
Find the largest prime number ![$p...
</a></td>
<td>
<span class=]() Algebra
Geometry
|
| 341 |
There exists a unique positive integer |
Algebra
|
| 340 |
Alice knows that ![$3$]() Probability
|
| 339 |
Let Algebra
Combinatorics
|
| 338 |
A piecewise linear function is defined by![]() |
Algebra
Geometry
|
| 337 |
The  Algebra
Combinatorics
|
| 336 |
The parabola with equation ![$y = ...
</a></td>
<td>
<span class=]() Algebra
Geometry
|
| 335 |
Sixteen chairs are arranged in a row. Eight peo...
|
Combinatorics
|
| 334 |
Let Combinatorics
Geometry
|
| 333 |
Let ![${\triangle ABC}$]() Algebra
Geometry
|
| 332 |
There are exactly three positive real numbers&n...
|
Algebra
|
| 331 |
Let Algebra
Combinatorics
|
| 330 |
The set of points in ![$3$]() |
Algebra
Geometry
|
| 329 |
Let ![]() |
Algebra
Geometry
|
| 328 |
The twelve letters ![$A$]() Combinatorics
Probability
|
| 327 |
Rectangles ![$ABCD$]() |
Geometry
|
| 326 |
Jen enters a lottery by picking ![...
</a></td>
<td>
<span class=]() Combinatorics
Probability
|
| 325 |
Alice and Bob play the following game. A stack ...
|
Combinatorics
|
| 324 |
Every morning Aya goes for a ![$9$...
</a></td>
<td>
<span class=]() Algebra
|
| 323 |
If the arithmetic mean of ![$a$]() |
Algebra
|
| 322 |
Triangle |
Geometry
|
| 321 |
What is the area of the region defined by the&n...
|
Algebra
Geometry
|
| 320 |
A permutation ![$(a_1,a_2,a_3,a_4,...
</a></td>
<td>
<span class=]() Combinatorics
|
| 319 |
A permutation ![$(a_1,a_2,a_3,a_4,...
</a></td>
<td>
<span class=]() Combinatorics
|
| 318 |
The equiangular convex hexagon ![$...
</a></td>
<td>
<span class=]() Geometry
|
| 317 |
A tetrahedron with four equilateral triangular ...
|
Geometry
Probability
|
| 316 |
If ![$S=1!+2!+3!+\cdots +99!$]() |
Algebra
|
| 315 |
The measures of the interior angles of a convex...
|
Algebra
Geometry
|
| 314 |
The measures of the interior angles of a convex...
|
Algebra
Geometry
|
| 313 |
![[asy] draw((0,0)--(10,20*sqrt(3)/2)--...
</a></td>
<td>
<span class=]() Algebra
Geometry
|
| 312 |
If  Algebra
|
| 311 |
Define an operation ![$\star$]() |
Algebra
|
| 310 |
Every morning Aya goes for a ![$9$...
</a></td>
<td>
<span class=]() Algebra
Combinatorics
Geometry
Probability
|
| 309 |
Rectangles ![$ABCD$]() |
Algebra
Geometry
Probability
|
| 308 |
Alice and Bob play the following game. A stack ...
|
Algebra
Combinatorics
Probability
|
| 307 |
Two geometric sequences ![$a_1, a_...
</a></td>
<td>
<span class=]() Algebra
Probability
|
| 306 |
In a certain year the price of gasoline rose by...
|
Algebra
Probability
|
| 305 |
Twenty percent less than 60 is one-third more t...
|
Algebra
Probability
|
| 304 |
For how many values of ![$x$]() |
Algebra
Combinatorics
|
| 303 |
A convex polyhedron ![$Q$]() |
Algebra
Probability
|
| 302 |
If the arithmetic mean of ![$a$]() |
Algebra
Geometry
Probability
|
| 301 |
The measures of the interior angles of a convex...
|
Algebra
Geometry
|
| 300 |
A circle passes through the vertices of a trian...
|
Algebra
Geometry
Probability
|
| 299 |
The real value of ![$x$]() Algebra
Probability
|
| 298 |
A particular ![$12$]() |
Algebra
Probability
|
| 297 |
Let ![$\mathcal{B}$]() |
Algebra
Geometry
Probability
|
| 296 |
Let  Algebra
Combinatorics
Probability
|
| 295 |
A number Algebra
Geometry
|
| 294 |
Distinct points ![$A$]() |
Algebra
Geometry
|
| 293 |
Triangle |
Algebra
Geometry
Probability
|
| 292 |
Each morning of her five-day workweek, Jane bou...
|
Algebra
Probability
|
| 291 |
By inserting parentheses, it is possible to giv...
|
Algebra
Probability
|
| 290 |
A region Algebra
Geometry
Probability
|
| 289 |
Trapezoid ![$ABCD$]() |
Algebra
Combinatorics
Geometry
Probability
|
| 288 |
For how many values of ![$x$]() |
Algebra
Combinatorics
|