Weekly Contest #6

(Ended)

Standings

Q1.

Using the letters A, M, O, S, and U, we can form five-letter "words". If these "words" are arranged in alphabetical order, then the "word" USAMO occupies position

Answer must be a floating-point or integer value and precision error less than 10^-6 is allowed.

Q2.

Question

Answer must be a floating-point or integer value and precision error less than 10^-6 is allowed.

Q3.

The Fibonacci sequence $1,1,2,3,5,8,13,21,...... starts with two 1s, and each term afterwards is the sum of its two predecessors. Which one of the ten digits is the last to appear in the units position of a number in the Fibonacci sequence?

Answer must be a floating-point or integer value and precision error less than 10^-6 is allowed.

Q4.

One thousand unit cubes are fastened together to form a large cube with edge length 10 units; this is painted and then separated into the original cubes. The number of these unit cubes which have at least one face painted is

Answer must be a floating-point or integer value and precision error less than 10^-6 is allowed.

Q5.

Question

Answer must be a floating-point or integer value and precision error less than 10^-6 is allowed.