An analogy: a child with blocks and constraints on physicalsystems. A certain child’s room is

partitioned into 100 squares. His toy box in the corner isexactly one square in size and contains

some number of blocks. When he plays with the toys, he tendsto throw them around and evenly

scatter them about the room.

a) Assume that there are now three blocks (red, green, andblue). Also assume that all three blocks

can fit on one square. How many accessible microstates arethere for this system, if they are all

in the toy box, lid is closed, and the lid is locked in theclosed position? (All the other constraints

imposed in the story still apply.)

b) What is the total number of accessible microstates for thissystem, if the toy-box lid is opened?

c) If the boy plays for a long time with all the blocks (andrandomly leaves them in the toy box or on

one of the floor squares), what is the probability of findingthe red block in the toy box, the blue

box on square #15, and the green block on square #75? Explainhow you determined this result.

d) Again, after a long time, what is the probability offinding the red block in the toy box independently

of where the blue and green blocks are?

e) How would probability in (d) change if we asked for itafter the boy had been playing for only 15

seconds? Explain why.

f) Explain what condition must be satisfied to say that asystem is equally likely to be in any of its

accessible microstates