A drawer contains exactly 5 red socks, 8 blue socks, 10 while socks, 12 green socks , and 7 yellow socks. Find the least number of socks to be chosen which will guarantee that there will be at least seven socks of the same color.

there's no way to pick 7 red socks, so it's a trick question.

Well, I can't be sure I'm right, but here's how I look at it.

Red
Blue
White
Green
Yellow

Each of the above is a color to choose from.

There is one that doesn't contain what you need, but you still have to take it into account so let's put that in first.

Red 5
Blue
White
Green
Yellow

Now it could be any color set of at least seven, which denotes seven or more socks.(I've never heard of this problem accounting for half a sock and will not hear it now. Also that's inconsequential in this particular problem.)

Red 5
Blue 7
White 7
Green 7
Yellow 7

Now, let's add that up. (7*4)+5= 33.
You need to pick 33 socks to be sure you have at leas seven of the same color.

For anyone looking at Steve's answer, please note that if they explicitly asked for 5 blue socks, the question would be a trick question. However, since they have to be "of the same color" and not "blue", we can calculate for any other color taking into account that there are blue socks that don't meet the minimum.

To find the least number of socks that will guarantee there are at least seven socks of the same color, we can use the Pigeonhole Principle. According to the principle, if there are n+1 objects to be placed into n boxes, then at least one box must contain more than one object.

In this case, we want to find how many socks we need to choose to guarantee that there are at least seven socks of the same color. We have five colors: red, blue, white, green, and yellow.

Worst case scenario: Let's assume we choose 6 socks of each color. In this case, we would have chosen a total of 6 x 5 = 30 socks.

To guarantee that there are at least seven socks of the same color, we can consider the worst-case scenario. In this case, we would have chosen 6 socks of each color, which totals to 6 x 5 = 30 socks. However, we still don't have seven socks of the same color.

Now, let's choose an additional sock. In the worst-case scenario, this new sock could be from any of the five colors. However, since we have already chosen six socks of each color, no matter which color the new sock belongs to, we will have at least seven socks of that color.

Therefore, the least number of socks that need to be chosen, guaranteeing that there will be at least seven socks of the same color, is 30 + 1 = 31 socks.

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