| 2481 |
AIME 2005 I Q3 |
How many positive integers have exactly three prop... |
1500.00 |
| 2482 |
AIME 2005 I Q4 |
The director of a marching band wishes to place th... |
1500.00 |
| 2483 |
AIME 2005 I Q5 |
Robert has 4 indistinguishable gold coins and 4 in... |
1500.00 |
| 2484 |
AIME 2005 I Q6 |
Let \(P\) be the product of the nonreal roots of \... |
1500.00 |
| 2485 |
AIME 2005 I Q7 |
In quadrilateral \(ABCD\), \(BC=8\), \(CD=12\), \(... |
1500.00 |
| 2486 |
AIME 2005 I Q9 |
Twenty seven unit cubes are painted orange on a se... |
1500.00 |
| 2487 |
AIME 2005 I Q11 |
A semicircle with diameter \(d\) is contained in a... |
1500.00 |
| 2488 |
AIME 2005 I Q12 |
For positive integers \(n\), let \(\tau (n)\) deno... |
1500.00 |
| 2489 |
AIME 2005 I Q13 |
A particle moves in the Cartesian Plane according ... |
1500.00 |
| 2490 |
AIME 2005 I Q15 |
Triangle \(ABC\) has \(BC=20\). The incircle of t... |
1500.00 |
| 2491 |
AIME 2005 II Q2 |
A hotel packed breakfast for each of three guests.... |
1500.00 |
| 2492 |
AIME 2005 II Q3 |
An infinite geometric series has sum \(2005\). A n... |
1500.00 |
| 2493 |
AIME 2005 II Q5 |
Determine the number of ordered pairs \((a,b)\) of... |
1500.00 |
| 2494 |
AIME 2005 II Q6 |
The cards in a stack of \(2n\) cards are numbered ... |
1500.00 |
| 2495 |
AIME 2005 II Q7 |
Let \[x=\frac{4}{(\sqrt{5}+1)(\sqrt[4]{5}+1)(\sqrt... |
1500.00 |
| 2496 |
AIME 2005 II Q8 |
Circles \(C_1\) and \(C_2\) are externally tangent... |
1500.00 |
| 2497 |
AIME 2005 II Q9 |
For how many positive integers \(n\) less than or ... |
1500.00 |
| 2498 |
AIME 2005 II Q10 |
Given that \(O\) is a regular octahedron, that \(C... |
1500.00 |
| 2499 |
AIME 2005 II Q11 |
Let \(m\) be a positive integer, and let \(a_0, a_... |
1500.00 |
| 2500 |
AIME 2005 II Q12 |
Square \(ABCD\) has center \(O\), \(AB=900\), \(E\... |
1500.00 |