Weekly Contest #9

(Ended)

Standings

Q1.

Question

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

Q2.

Eight people are sitting around a circular table, each holding a fair coin. All eight people flip their coins and those who flip heads stand while those who flip tails remain seated. What is the probability that no two adjacent people will stand?

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

Q3.

At a gathering of 30 people, there are 20 people who all know each other and 10 people who know no one. People who know each other hug, and people who do not know each other shake hands. How many handshakes occur within the group?

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

Q4.

Question

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

Q5.

When Jon Stewart walks up stairs he takes one or two steps at a time. His stepping sequence is not necessarily regular. He might step up one step, then two, then two again, then one, then one, and then two in order to climb up a total of 9 steps. In how many ways can Jon walk up a 14 step stairwell?

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