Daily Test ~ {ERG}

[LoneRanger]

30 August 2008:

THE SOLUTION:

One way to solve this maze puzzle is to realize that at each marked intersection (or decision point), the marble has a 50-50 choice (or 1/2 chance) of going right or left. There are three paths by which the marble can get to the winning exit (1-2-6-8, 1-2-4-6-8, and 1-3-5-4-6-8). All we need to do is multiply the 1/2 probabilities at each decision point along each path to find the likelihood of traveling a particular path. So for the three paths we have (1/2 x 1/2 x 1/2 x 1/2) + (1/2 x 1/2 x 1/2 x 1/2 x 1/2) + (1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2). Thus, we find 1/16 + 1/32 + 1/64 which is about 0.11—only about an 11 percent chance of winning!



Sally is looking at a sushi menu. To make a single piece of sushi, she can choose tuna, squid, or shrimp, which can be either in the form of a roll or sliced. In addition, the piece may be either plain or coated with red, black, white, or green caviar. How many different pieces of sushi can Sally make?