Maths Puzzle :: Discussion

There are 10 colors of socks in a dark room such that…
color 1 > 2 socks
color 2 > 4 socks
color 3 > 6 socks
color 4 > 8 socks
And so on… up to color 10 such that color 10> 20 socks. How many minimum numbers of socks you have to bring out of that dark room such that 6 socks must be of the same color? Given the condition that there is no light to switch on in that room.
Explanation :
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Consider you picked 6 socks randomly from all of them and assume that you have picked 2 socks of color 1 and 4 socks of color 2.
Let’s assume this x=6.
Now from remaining colors that is from color 3 to 10, you have to pick some socks such that you will get 5 socks of each color.
That is 5 *(number of remaining colors)=5*8=40. Let’s assume this y=40.
Now comes the last step of the answer. After performing the first and second step, If you pick any 1 socks from remaining socks you will satisfy the criteria of the question. Because you already have 5 socks from each of the color bracket(color 3 to color 10).If you pick any 1 socks it will belong to one of this color bracket. and you will get 6 socks of the same color. Let’s assume this z=1.
so the final answer is x+y+z=6+40+1=47. So you have to bring minimum 47 socks from the darkroom to satisfy question criteria.