Question 551404: Could you please help me with this question?:(Mady has an infinite number of balls and empty boxes available to her. The empty boxes, each capable of holding four balls, are arranged in a row from left to right. At the first step, she places a ball in the first box of the row. At each subsequent step, she places a ball in the first box of the row that still has room for a ball and empties any previous boxes. How many balls in total are in the boxes as a result of Mady’s 2010th step?)I tried to do this problem by trying to find a formula for calculating how many steps she takes to fill a box. It didn't work and I do not understand a different way to solve this problem.
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Try the first several steps to understand what is going on here. The numbers 0-4 represent the number of balls in each box:
Step---#
1------10000
2------20000
3------30000
4------40000
5------01000
6------11000
7------21000
8------31000
9------41000
10-----02000
11-----12000
.
.
.
If you know how to count in different bases such as binary or hexadecimal, it shouldn't take long to conclude that the pattern relies entirely on base 5, (except with digits reversed, but the ordering of the digits is irrelevant). 2010 in base 5 is 31020, so the number of balls in the boxes is 3+1+2 = 6.
Tip: If you don't know what "bases" are, keep in mind that the normal counting we do is in base 10. You may want to read the following:
http://en.wikipedia.org/wiki/Base_(exponentiation)
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