There is a drawer which contains 12 pairs of blue gloves, 12 pairs of grey and 12 pairs of black. What is the minimum number of gloves that should be picked to ensure that at I pick at least one pair of gloves of each colour
I chose $12$ right hand gloves of each colour - blue, grey and black. and then selected $3$ left hand gloves of each colour. Total=$39$.
What is wrong with my solution?
If you can distinguish left and right by touch but not by sight, you can make sure you have a right-hand glove of each colour by pulling out $25$ gloves. Then pulling out a left-hand glove will make at least one pair. For a pair of each colour you need to pick out $25$ left-hand gloves to make sure that each colour is covered. Total $50$.
If you can't distinguish between left and right, you might pull out all the blue and grey gloves - a total of $48$ and then all the twelve black right-hand gloves before you pick (finally) a left-hand one to complete the final pair. Total $61$.
If we had socks instead, we might pick out all the blue and grey ones - total $48$ before picking any black ones. We need two black to make a pair, so $50$ are required.