Alg / NT
What is the last digit of 1001^1001?
1
What is sin^2 (pi/8) + cos^2 (pi/8) + tan^2 (pi/8) - sec^2 (pi/8)?
0
Three 8-sided dice are rolled. What is the probability that they all return the same value?
1/64
Find the largest three-digit number which is not a multiple of 3, but is a multiple of the sum of its digits.
[SMT Discrete Tiebreaker]
935
Each team selects an integer from 1 to 100 simultaneously. The closest team to half the average gains 100 points, but if any team gets 4x the average, they get 500 points.
:3
There exists some integer x such that x^25 = 1,341,068,619,663,964,900,807. What is x?
7
AX = 6 is a tangent to circle w and AY = 12 is a secant to circle w. AY intersects w at a point Z different from Y. Determine YZ.
9
free square :3
+200 points
What is the maximum number of unit circles that can be outwardly tangent to a circle with radius 99?
In what year did the spacecraft Sputnik successfully launch?
1957
Given x + 1/x = 10, what is x^3 + 1/x^3?
970
What is the period of:
sin(cos(cos(pi*x))) + cos(cos(sin(2pi*x))) + sin(cos(sin(3pi*x)))
1
99 8-sided dice are rolled. What is the probability that the resulting sum is even?
1/2
Bridget and Miku play a game on a circular board with radius X, and a small circular hole cut out of the center of radius Y < X. They take turns placing unit circles on the table, with Bridget going first. Placed unit circles must not overlap previously placed circles and must be completely on the board. The last person to have a legal move wins. Assuming perfect play, which is true?
(A) Bridget always wins
(B) Bridget wins only if Y < 0.75X
(C) Bridget wins only if Y < 0.5X
(D) Bridget wins only if Y < 0.25X
(E) Miku always wins
Name 7 unsolved problems in mathematics.
:3
The number 36742000 has a total of 40 factors. How many factors does the number 367420000 have?
60
Rectangle ABCD has side lengths AB = 10 and BC = 12. Let the midpoint of CD be point M. Compute the area of the overlap between AMB and ADC.
[SMT Geo TB]
20
On average, how many times do you have to flip a coin until you flip three heads in a row?
14
[Price is Right - Highest correct team wins]
Consider the following game. Nova starts at (0, 0) and moves to any point up to X units away. Then, Celeste places a disk of radius 1 onto the board such that Nova is not within the disk. Nova can't move into or on disks on all future turns. Celeste wins if they can trap Nova. What is an X that allows Celeste to win?
All X <= 3 are correct.
CHAOS WHEEL >:3333
>:3
Compute:
5 / (1*2*3*4) + 7 / (2*3*4*5) ... 99 / (48*49*50*51)
[SMT Alg Round]
832/2499
Up to reflections and rotations, how many unique cyclic quadrilaterals with perimeter 12 and integer sides are there?
8
Each vertex and edge of an equilateral triangle is randomly labelled with a distinct integer from 1 to 10, inclusive. Compute the probability that the number on each edge is the sum of those on its vertices.
[SMT Discrete Round]
1/1680
Prove or disprove that there exists only one shape up to scaling that has the property that any chord drawn between two points that cover some set length along the shape's perimeter is the same length no matter where that perimeter is. (Credit: Sylvia)
Proof goes as follows (may vary):
Consider the perimeter length 1/n. Then, the resulting shape of three such chords will form a regular n-gon. In other words, our shape must inscribe all regular n-gons. But, as n approaches infinity, n-gons become closer and closer to circles. Thus, the only possible shape is a circle.
Answer an Esoteric Problem :3 (or lose 500 points)
>:3