MathDB

8

Part of 2014 ASDAN Math Tournament

Problems(5)

2014 Advanced #8

Source:

7/1/2022
Nick has a 3×33\times3 grid and wants to color each square in the grid one of three colors such that no two squares that are adjacent horizontally or vertically are the same color. Compute the number of distinct grids that Nick can create.
2014Advanced Topics Test
2014 Algebra #8

Source:

7/8/2022
Consider the recurrence relation an+3=an+2an+1−2ana_{n+3}=\frac{a_{n+2}a_{n+1}-2}{a_n} with initial condition (a0,a1,a2)=(1,2,5)(a_0,a_1,a_2)=(1,2,5). Let bn=a2nb_n=a_{2n} for nonnegative integral nn. It turns out that bn+2+xbn+1+ybn=0b_{n+2}+xb_{n+1}+yb_n=0 for some pair of real numbers (x,y)(x,y). Compute (x,y)(x,y).
2014Algebra Test
2014 General #8

Source:

7/4/2022
George and two of his friends go to a famous jiaozi restaurant, which serves only two kinds of jiaozi: pork jiaozi, and vegetable jiaozi. Each person orders exactly 1515 jiaozi. How many different ways could the three of them order? Two ways of ordering are different if one person orders a different number of pork jiaozi in both orders.
2014General Test
2014 Team #8

Source:

7/1/2022
Equilateral triangle DEFDEF is inscribed inside equilateral triangle ABCABC such that DEDE is perpendicular to BCBC. Let xx be the area of triangle ABCABC and yy be the area of triangle DEFDEF. Compute xy\tfrac{x}{y}.
2014team test
2014 Geometry #8

Source:

7/12/2022
Moor made a lopsided ice cream cone. It turned out to be an oblique circular cone with the vertex directly above the perimeter of the base (see diagram below). The height and base radius are both of length 11. Compute the radius of the largest spherical scoop of ice cream that it can hold such that at least 50%50\% of the scoop’s volume lies inside the cone.
2014Geometry Test