balls in boxes counting problem

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?

This would involve modular arithmetic but not sure how to solve it. Any idea appreciated. Thanks!

score 1 · Accepted Answer · edited Feb 15 '20 at 08:07

If I understand correctly, Mary is counting up in base 5. Example:

Right <------------- Left
......00000001 First Step
......00000002 Second Step
......00000003 Third Step
......00000004 Fourth Step
......00000010 Fifth Step
......00000011 Sixth Step

So I believe you should find the representation of 2010 in base 5 and add the digits together, e.g. $(2010)_{10} = (31020)_5$ so my answer would be 6 balls.

balls in boxes counting problem

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