A certain road has a path of a perfect circle with a single entrance/exit. A woman enters the road and walks the full circumference at a constant speed without stopping or changing direction. During her time on the road, N cars, each at its own random time during the duration of the walk, enter the circle. Each car proceeds, on the shortest path, to its own randomly selected stopping point on the circle. If cars travel 10 times as fast as the woman walks, answer the following:
1) For N=1, what is the probability that the woman “encounters” a car?
Definition: An “encounter” is when a moving car either overtakes the woman in the same direction or passes her while going in the opposite direction. If a car is stationary, there can be no encounter.
2) What is N such that there is at least a 75% chance of encountering a car?
3) For N=20, what is the expected number of encounters?
A science fiction show of many years ago, showed what we would today call SETI scientists receiving numeric signals from what was determined to be an extraterrestrial civilization. They were the repeated digits 3 1 4 1 5 9 2 6 5 3.What if the signals had been 6 3 4 9 4 1 6 9 6 7 11 6 that kept repeating? Would you recognize the set? What is it as a signal of an ET civilization?
If you need more hints than this, swipe the rest of this puzzle to see two more sequences from the same civilization, printed to match the background to hide them while trying to solve from just the above.
There are many kinds
