Missy and Mussy's Socks

Consider the maximum number of socks you can take out without getting 4 of the same colour, which is to have 3 of each colour (except only 2 blacks since there are only 2). The number of socks then would be 3+2+3+3=11. Any sock after that would give 4 of the same colour, so the minimum to guarantee is 12.

The maximum number of socks where no four socks are of the same colour would be 3 socks per colour. However, since there are only 2 black socks, that number is 3 (white) + 2 (black) + 3 (blue) + 3 (red) = 11. The next sock you'd draw would have to be white, blue or red, which would complete a set of four. Therefore, the number of socks you need to remove from drawer is 11 (max number not satisfying the condition) + 1 = 12.

Let us consider the worst-case scenario possible: They draw three socks from each color before drawing the fourth sock. If there are infinitely many socks of each color, then the answer would be 4*3+1=13. However, we are only given 2 black socks instead of infinitely many, so we subtract (3-2)=1 from 13 to arrive at the final answer of 12.

Missy and Mussy removes the socks one by one. The worst scenario that they face before obtaining 4 socks of the same color is: 2 black socks, 3 white socks, 3 blue socks and 3 red socks. Therefore, the next sock that they remove must be white, blue or red (it cannot be black there are only 2 of them), which satisfies the condition (4 socks of the same color). Hence, to be sure, they need to remove at least $2 + 3 + 3 + 3 + 1 = 12$ socks to certainly obtain 4 socks of the same color.

First one sock is removed. It can be either of the four colours. The next sock removed can also be of any colour. For the extreme* case, let the two socks removed be black (since they are least in number). Then the next sock can be of 3 colours. Again, for the extreme case, let the next nine socks be of the remaining colours such that every 3 socks are of same colour (i.e., 3 white socks, 3 blue socks and 3 red socks). This is done to ensure that there are no 4 socks of same colour. Now, whatever be the next sock removed, it has to be any of the colours white, blue or red. Hence, now there are 4 socks of the same colour. Therefore, minimum 12 socks has to be removed.

Extreme case has been taken because in any other case, 4 socks of the same colour appear in less than 12 removals.

You must draw 3 of each sock before drawing a 4th sock, which would make it certain you have 4 of the same color. And since you can only draw 2 black socks, you add 2. So you get the 3 white + 2 black + 3 blue + 3 red, which is 11 socks. Then you add the 4th one = 12 socks. After you draw the 12th sock can you be certain you have drawn 4 socks of the same color.

First note that they cannot have 4 black socks. In the worst case scenario, they pick both black socks, 3 white socks, 3 blue socks, and 3 red socks, so that they have no 4 socks of the same color, and that when they pick their next sock, which must be white, blue, or red, they will have 4 socks of the same color. In this scenario, 2+3+3+3=11 socks have been chosen, and choosing one more leads to the answer, 12 socks.

First, we note that it's impossible to get 4 black socks (because there's only 2) so we can immediately take those out of the dresser for 2 socks. This also removes the color black, meaning there are only three colors left.

We then remove the maximum number of socks from each color that avoids fulfilling the condition. To do this, we draw 3 socks from each of the three colors that remain, for an additional 9 socks drawn.

Since the problem asks for the minimum to fulfill the condition, we must draw one last sock of any color to make that color's total four. Thus, the minimum number of socks that must be drawn is 3+3+3+2+1=12.

4-1=3 3+2+3+3=11+1=12

we can remove 2 black socks, 3 white ones,3 blue ones and 3 red ones. now if we remove 1 more sock it must be of the red/blue/white color making the no of socks of that particular color=4 so total moves=2+3+3+3+1=12 (ans)

Without regard to order pick a sock as long as it doesn't complete a set of 4. We could pick 2 black socks and 3 of each of the other colours, 11 socks. At this point any selection made will complete a set and so the answer is 12.

see,considering the worse case,she pics up 3 white 3 blue 3 red 2 black socks ,now she pics one more sock,she will get four
socks of same colour..........

The unluckiest and the most exhaustive efforts should be considered when answering a question of certainty with the presence of the word "minimum" and phrases like "in order to be certain" and those of similar meaning.

"Their dresser drawer consists of 43 white socks, 2 black socks, 23 blue socks and 8 red socks."

A success is defined by "the removal of four socks of the same (of any possible) colour", so with all 4 available colours, the assortment of failures would be
= Failed whites + failed blacks + failed blues + failed reds
= Σ min[4 – 1, available number of socks] {for each colour}
= 3 whites + 2 blacks + 3 blues + 3 reds
= 11 socks

So the unluckiest drawings would be 11 socks without any 4 of the same colour (in contrast to the lucky first 4 being 4 reds or 4 blues or 4 whites), but the 12th draw of either a red or a blue or a white will finally give us the elusive success.

For now, let us ignore the black socks(2) as its quantity is less than 4. Now we have to choose the 4 socks from the rest of the socks. Lets consider there are three pigeonholes(white, blue and red). Lets take 9 pigeons( corresponding to 9 non- black socks ). Its possible to arrange these 9 pigeons in the 3 holes such that each hole has no more than 3 pigeons. But if you take 10 pigeons, then at least one pigeonhole has 4 or more pigeons in it. So "10" could have been our answer. But as the black socks(2) are also present , it is possible that the black socks might have been present in those 10 pigeons(which were assumed to be non-black socks). So to make sure there are at least 10 non-black socks present in the removed heap of socks, removed heap should have 10 + 2(quantity of black socks) = 12 socks.

if u can't understand these given explanation then, my friend go and read the tutorial again.

The number of socks having same colour and more than four are only three .that means white,blue,black.therfore we must remove the socks from the drawer having above colours .so we want to remove three colours of socks each colour having four socks 3(4) is equal to 12