Puzzle Details :
A man has 53 socks in his drawer: 21 identical blue, 15 identical black, and 17 identical red. The lights are out and he is completely in the dark. How many socks must he take out to make 100 percent certain he has at least one pair of black socks?
Solution :
To answer such questions we always have to assume that the worst-case scenario has occurred. if the worst-case scenario is covered all other scenarios have definitely been covered.
So in this case lets assume:
- The first 21 socks he takes out are all blue
- The next 17 socks he takes out are all red
Since now only black socks remain in the drawer the next 2 socks he will draw will surely be black.
So, the total number of minimum socks he has to take out to be absolutely sure that he has a pair of black socks is 21+17+2 = 40
40 socks. If he takes out 38 socks (adding the two biggest amounts, 21 and 17), although it is very unlikely, it is possible they could all be blue and red. To make 100 percent certain that he also has a pair of black socks he must take out a further two socks.
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