Challenge question #57 (14/08/2017)
Anne, Bill, Chen, and Dwayne need to travel from one side of a bridge to the other. The bridge can only hold two people at a time. It is very dark, and the group has one torch which must be carried back and forth as people cross the bridge.
Anne takes $1$ minute to cross the bridge, Bill takes $2$ minutes, Chen takes $5$ minutes, and Dwayne takes $10$ minutes.
What is the quickest time in which the whole group can get across the bridge?
A paddock contains $6$ gates as shown alongside.
The farmer can choose to either open or close each gate. He then chooses one of the enclosed areas in which to place his cow.
In how many ways can this be done?