Answer:
The number of balls in the box at 2010th step is 6 balls
Explanation:
Since the boxes are arranged from left to right, and since the empty boxes are capable of holding 4 balls at once.
Therefore, her steps would follow this pattern ;
00001 - 1st Step
0002 - 2nd Step
0003 - 3rd Step
0004 -4th Step
0010 - 5th Step
0011 - 6th Step
0021 - 7th step
0031 - 8th step
0041 - 9th step
Looking at this pattern, it is obvious this digits are in base 5 because once we count to 4 in a unit, we move to the next at 1.
Thus,at Mady's 2010th step, we'll convert to base 5,thus 2010 in base 5 is calculated as;
2010 ÷ 5 = 402 r 0, so Base 5 is now: _ _ _ _ 0.
402 ÷ 5 = 80 r 2, so Base 5 is now: _ _ _ 2 0.
80 ÷ 5 = 16 r 0, so Base 5 is now:
_ _ 0 2 0.
16 ÷ 5 = 3 r 1, so Base 5 is now: _ 1 0 2 0.
3 ÷ 5 = 0 r 3, so Base 5 is now: 3 1 0 2 0.
So 2010 in base 10 is 31020 in base 5. Thus,the number of balls in the box at 2010th step is equal to 3 + 1 + 0 + 2 + 0 = 6balls
