Problem Solving

In a jar there are 21 white balls, 24 green balls and 32 blue balls.
How many balls must be taken out in order to make sure that we have 23 balls of the same color?
a) 23
b) 46
c) 57
d) 66
e) 67

Good question...

66 balls

21 white + 22 green + 23 blue or
21 white + 22 blue + 23 green

nithi_mystics wrote:66 balls

21 white + 22 green + 23 blue or
21 white + 22 blue + 23 green

Thanks Nithi.But give the explanation for clear idea.

nithi_mystics wrote:66 balls

21 white + 22 green + 23 blue or
21 white + 22 blue + 23 green

thanks.....but explain me clearly..... i can't understood your logic.......

The answer should be 66.
Here's how:
In solving this kind of problems we should consider the worst case scenario, i.e. what will make me draw more balls out of the jar or what will delay my process of getting 23 balls of the same color.
Note that we have only 21 white balls and hence can never have 23 white balls. Thus 21 white balls are there just to make your target worse
Suppose you pick up the first 21 balls (if you are wondering how I decide on the number 21, note that we have only 21 white balls) and they all turn out to be white. Then you keep on picking balls but the next 21 turn out to be green; while the next 21 turn out to be blue. Thus after 21*3=63 draws you have 3 sets of 21 balls each of colors white, green and blue.
Now, we do not have anymore white balls, hence the next draw has to be blue or green. Suppose it's green while the subsequent draw is blue (remember you need to think about the worst case). So, we have 22 balls each of green and blue colors. One more ball will ensure that I have either 23 green or 23 blue balls.
Thus total number of draws from the jar is : 63 + 2 + 1 = 66

Hope this helps.

Thanks
Anirban