Sipnayan C

The angles in a quadrilateral are in the ratio 2: 5: 5: 6. What is the difference between the measure of the largest angle and the measure of the smallest angle in the quadrilateral?

Answer Format: __ degrees

Bonnie starts with 1 whole hotdog, but she wants to savor the flavor. So, in her first bite, she eats of the hotdog. Then, in her second bite, she eats of the 1 2 1 3 remaining hotdog. Then, in her third bite, she eats of the remaining hotdog, 1 4 and so on. What fraction of the hotdog is left over after Bonnie’s 2019th bite?

Answer Format: _/_

(Fraction)

In the figure below, triangle 𝐿𝑇𝑅 has sides 𝐿𝑇 = 70 𝑐𝑚 and 𝐿𝑅 = 79 𝑐𝑚. 𝐼, 𝐺, 𝐻 are points on 𝐿𝑇 while 𝑌, 𝐸, 𝐴 are points on 𝐿𝑅 such that triangles 𝑇𝑅𝐻, 𝑅𝐻𝐴, 𝐻𝐴𝐺, 𝐴𝐺𝐸, 𝐺𝐸𝐼, 𝐸𝐼𝑌, 𝑎𝑛𝑑 𝐼𝑌𝐿 have the same area. Find the length of 𝐼𝐻.

Answer Format: __ cm

The numbers from 1 to 2019 are placed side-by-side to have the number 123456789101112…2016201720182019

How many times will the digits “21” appear in this number?

In a geometric figure, 5 equilateral triangles are placed on a regular pentagon. One side of an equilateral triangle is placed on top of one of the sides of the regular pentagon so that the two other sides of the equilateral triangle are outside the regular pentagon. If the perimeter of the geometric figure is 2019 meters, what is the perimeter of the regular pentagon?

Answer Format: _ meters

Suppose a 9-sided die is constructed and is rolled. There are 8 faces of the die that can be seen. What is the probability that the product of the numbers on the 8 faces of the die is divisible by 64?

Answer Format: _/_

Fraction

The numbers from 0 to 100 are written down in order:

01234567891011...979899100

If we pick out three consecutive digits to form a three-digit number such that the hundreds and tens digit have a sum of 10, then what is the sum of all the possible units digit?

Suppose the faces of a rectangular box with dimensions 8×9×10 are painted red. The box is the sliced into 1×1×1 cubes. How many of these cubes have exactly 2 faces painted red?

Given the infinite string "21NFINITY21NFINITY...", find the 2019th character in the string.