Gloves in the dark

Question

A drawer contains 10 pairs of black gloves and 10 pairs of white gloves: that is 40 gloves, half of them left-handed and half right-handed. It is dark; you can feel neither colour nor handedness. How many gloves must you take out to be certain of having a wearable pair, meaning one left glove and one right glove of the same colour? Socks would need only three. Gloves are worse. Why?

Accepted Answer

21 gloves. Twenty is not enough. There are 20 left-handed gloves in the drawer (10 black, 10 white). You could pick all 20 of them before touching a single right-handed glove, and 20 left gloves contain no wearable pair. So a guarantee needs more than 20. Twenty-one always works. Take any 21 gloves. Since there are only 20 gloves of each handedness, you must hold at least one left glove and at least one right glove; more precisely, you hold at least 11 of one handedness and at least 1 of the other. Call the majority handedness "left". Now consider the colour of any right glove you hold. If yo…

Gloves in the dark

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