Cody

Problem 44719. Penny Distribution Machine

A machine consists of a row of boxes. To start, one 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 one box 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, the figure below shows the working of the machine in distributing nine pennies by always selecting a pair of pennies in the leftmost box with at least two coins.

Itr 0:   9  0  0  0        
Itr 1:   7  1  0  0 
Itr 2:   5  2  0  0  
Itr 3:   3  3  0  0  
Itr 4:   1  4  0  0   
Itr 5:   1  2  1  0   
Itr 6:   1  0  2  0   
Itr 7:   1  0  0  1  

Determine the number of boxes and iterations needed by the machine to distribute N pennies. From the example above, the machine requires four boxes and seven iterations to distribute nine pennies.

Solution Stats

63.64% Correct | 36.36% Incorrect
Last solution submitted on Feb 08, 2019

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