# How many socks do you need to pick ?

+1 vote
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In your bedroom, you have a drawer with 2 red, 4 yellow, 6 purple, 8 brown, 10 white, 12 green, 14 black, 16 blue, 18 grey, and 20 orange socks. It is dark in your bedroom, so you cannot distinguish between the colors of the socks.How many socks do you need to take out of the drawer to be sure that you have at least three pairs of socks of the same color?

posted Apr 24, 2014

## 1 Solution

47
10 of different colors ,and then you pick remaining red (so you have 11) and then you pick three yellow(so you have 14) and you still have one pair of red and two pairs of yellow,
then one of each of the remaining that would be 8. (one pair of red, 2 pairs of yellow, 1 pair of each of the others) and another 8 of remaining twice (you will have 2 pairs of each of them) + another 8 of remaining +1

10(all diff) + 4(one red+3 yellow) + 8(one of each of remaining) -- one pair of each color
+ 8(all of diff colors) + 8 (all diff colors) -- 2 pairs of diff colors
+ 8 (all diff colors) + 1

= 47

solution Apr 25, 2014

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A trip around the world!
Logic Level 3

There is an air base on the equator. The maximum amount of fuel that a plane can contain would be only sufficient for it to fly halfway around the world.

For at least one plane to finish a trip around the world, how many planes do you need at least?

Details and assumptions:
Same plane doesn't depart twice or more.
The airplanes can use their fuel until it's empty. Starting the airplane doesn't take any time.
Every plane moves at the same speed, and on the same airway.
Assume the planes and air base are dimensionless, and thus, can turn directions instantly.
The plane can only be fueled via aerial refueling, and the amount of time the process takes is negligible.
Every plane starts at the air base and must return to the air base.