Question 1198918
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B = blue
G = green
R = red


4 pairs = 4*2 = 8 individual socks
Of course it's impossible to have 4 pairs of red, since Toni simply doesn't have enough red socks.
Therefore, she'll either have 8 blue or 8 green.


The best case scenario is that Toni selects 8 blue socks in a row, or 8 green socks in a row. 
This would be the minimum number of selections needed.
This is if she gets really lucky. 


But we cannot assume this incredible luck and instead have to consider the worst case scenario, so that we 100% guarantee getting those 4 matching pairs.


The worst case scenario is her selecting say a blue sock first, then green, then red. 
It would give the sequence: B, G, R.
The order doesn't really matter. 
All that matters is that she doesn't have a matching pair yet.


The 4th selection changes that since she has no other colors to pick from. 
This 4th selection is guaranteed to be a match with a previous selection. 
Refer to the pigeonhole principle.


Let's say the 4th selection was red. 
Then let's say the 5th and 6th selections were also red. 
This means she has chosen all 4 red socks.


But as I mentioned earlier, we ignore red since there aren't enough red socks to make 4 pairs that match.


We have this sequence so far
B, G, R
R, R, R



For the 7th selection we could go for blue or green. 
Let's have the colors alternate to guarantee the worst case scenario. 
This delays a matched pair as much as possible.


She has selected 1 blue sock so far.
There are 10-1 = 9 blue socks left.
She needs 8-1 = 7 more blue socks to have 4 pairs of blue.


She has selected 1 green sock so far.
There are 14-1 = 13 green socks left.
She needs 8-1 = 7 more green socks to have 4 pairs of green.


In short: she needs 7 more of either green or blue.


The worst case scenario is that she selects 6 green and 6 blue in any order you want.
That's an additional 6*2 = 12 socks on top of the 6 already chosen.
There are a total of 6+12 = 18 socks selected so far.


By the <font color=red>19</font><sup>th</sup> selection, she has 4 pairs of the same color (aka 8 socks of the same color). 
We don't have enough information to determine if the 4 matching pairs would be blue or green.



Answer: <font color=red>19 (choice D)</font>


Bonus question to think about: 
What is the least number of socks that Toni needs to select to guarantee 4 pairs of blue and 4 pairs of green?


Edit: The tutor @greenestamps offers a more streamlined approach. And it makes sense to get the red socks out of the way first, which I didn't consider.
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