<h3>
Answer: 24</h3>
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Explanation:
If Jack were to get really lucky and draw either
* 8 red balls in a row
* 8 green balls in a row, or,
* 8 white balls in a row
then the answer would be 8. However, this event of drawing the same color ball 8 times in a row is fairly unlikely. What is more likely is that there will be multiple colors involved (because we have roughly the same number for each color mors or less). So consider the scenario in the next section below.
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If Jack were to draw a red ball first, then a green ball second, and then a white ball third, then so far has selected 3 balls from the drawer. None of the colors match up. This is leading to the worst case scenario in terms of the number of balls to select. In other words, Jack is really unlucky to not get any colors match up so far. When aiming for a guarantee like this, it is wise to think of the worst case scenario.
If we repeat the pattern (red, green, white) then so far we have 2 balls of each color. In total we have selected 6 overall. Note how 3*2 = 6.
Repeat this a third time, then we'll select 9 balls total (3*3 = 9)
The fourth iteration of this pattern has 3*4 = 12 balls overall picked out, and so on.
If we continue the pattern, then we'll see that we will need to select 3*8 = 24 balls to guarantee that we have at least 8 of the same color (eg: 8 red balls). Chances are that we'll have 8 of the same color before we hit the 24 ball mark, but we wont have a 100% guarantee of such. Reaching 24 balls is the only way to guarantee the claim is true.
So to summarize: I pictured the worst case scenario (red,green,white) and extended out the pattern so that it led to 24 as the final answer.
