MathDB

5

Part of 2015 ASDAN Math Tournament

Problems(5)

2015 Advanced #5

Source:

7/8/2022
Four men are each given a unique number from 11 to 44, and four women are each given a unique number from 11 to 44. How many ways are there to arrange the men and women in a circle such that no two men are next to each other, no two women are next to each other, and no two people with the same number are next to each other? Note that two configurations are considered to be the same if one can be rotated to obtain the other one.
2015Advanced Topics Test
2015 Algebra #5

Source:

7/1/2022
The Fibonacci numbers are a sequence of numbers defined recursively as follows: F1=1F_1=1, F2=1F_2=1, and Fn=Fn−1+Fn−2F_n=F_{n-1}+F_{n-2}. Using this definition, compute the sum ∑k=110FkFk+1Fk+2.\sum_{k=1}^{10}\frac{F_k}{F_{k+1}F_{k+2}}.
2015Algebra Test
2015 Guts #5

Source:

7/28/2022
Compute the number of zeros at the end of 2015!2015!.
2015Guts Test
2015 Geometry #5

Source:

7/1/2022
The eight corners of a cube are cut off, yielding a polyhedron with 66 octagonal faces and 88 triangular faces. Given that all polyhedron's edges have length 22, compute the volume of the polyhedron.
2015Geometry Test
2015 Team #5

Source:

8/3/2022
Laurie loves multiplying numbers in her head. One day she decides to multiply two 22-digit numbers xx and yy such that x≤yx\leq y and the two numbers collectively have at least three distinct digits. Unfortunately, she accidentally remembers the digits of each number in the opposite order (for example, instead of remembering 5151 she remembers 1515). Surprisingly, the product of the two numbers after flipping the digits is the same as the product of the two original numbers. How many possible pairs of numbers could Laurie have tried to multiply?
2015team test