A machine consists of a row of boxes sidebyside To start the

A \"machine\" consists of a row of boxes side-by-side. To start the machine, the user places n pennies in the leftmost box. The machine then redistributes the pennies as follows. On each iteration, it replaces a pair of pennies in the leftmost box with at least two coins with a single penny in the next box to the right. The iterations stop when there is no box with more than one coin. For example, if we start with 6 pennies in the leftmost box, we get the sequence What will be the final distribution of pennies if we start with 17 pennies in the leftmost box? Justify your answer. What is the minimum number of boxes needed to distribute n pennies? Justify your answer.

Solution

a)

if we start with 17 pennies in the leftmost box the final distribution of pennies will be

1 interation 15

2 interaction 13

3 interaction 11

and so on

b)

will be n=2 because in the first interaction you will take 2 pennies