MathDB

7

Part of 2014 ASDAN Math Tournament

Problems(5)

2014 Advanced #7

Source:

7/1/2022
Two math students play a game with kk sticks. Alternating turns, each one chooses a number from the set {1,3,4}\{1,3,4\} and removes exactly that number of sticks from the pile (so if the pile only has 22 sticks remaining the next player must take 11). The winner is the player who takes the last stick. For 1≤k≤1001\leq k\leq100, determine the number of cases in which the first player can guarantee that he will win.
2014Advanced Topics Test
2014 Algebra #7

Source:

7/8/2022
f(x)f(x) is a quartic polynomial with a leading coefficient 11 where f(2)=4f(2)=4, f(3)=9f(3)=9, f(4)=16f(4)=16, and f(5)=25f(5)=25. Compute f(8)f(8).
2014Algebra Test
2014 General #7

Source:

7/4/2022
Ben works quickly on his homework, but tires quickly. The first problem takes him 11 minute to solve, and the second problem takes him 22 minutes to solve. It takes him NN minutes to solve problem NN on his homework. If he works for an hour on his homework, compute the maximum number of problems he can solve.
2014General Test
2014 Team #7

Source:

7/1/2022
Eddy draws 66 cards from a standard 5252-card deck. What is the probability that four of the cards that he draws have the same value?
2014team test
2014 Geometry #7

Source:

7/12/2022
Let ABCDABCD be a square piece of paper with side length 44. Let EE be a point on ABAB such that AE=3AE=3 and let FF be a point on CDCD such that DF=1DF=1. Now, fold AEFDAEFD over the line EFEF. Compute the area of the resulting shape.
2014Geometry Test