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 (the leftmost 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 boxes to its left. How many balls in total are in the boxes as a result of Mady's 2010th step?

vockeyvockvock Feb 17, 2021

#1**0 **

Hi vockeyvockvock (your username is very fun to say)!

So, let's try visualizing this box scenerio.

10000000

20000000

30000000

40000000

01000000

11000000

21000000

31000000

It becomes like counting in base 5. But, the numbers are reversed. (1, 2, 3, 4, 10, 11, 12, 13, 14, ...)

So we just need to convert 2010 into base 5 and sum the digits, 31020. (Normally, I'd put a link to a video explaining how to convert bases, but my posts keep getting flagged because of it.)

Now we just add the digits, 3+1+0+2+0 = 6.

6 is our answer. :))))

=^._.^=

catmg Feb 17, 2021