Coloured coins in the dark
You are in a dark room. On a table in front of you are 500 coins. Each coin is red on one side and black on the other. The coins have been set up so that 100 have their red side showing and 400 their black side uppermost. Your job is to produce two groups of coins from this lot which have the same number of red sides uppermost. You can turn the coins updside down in the dark, shuffle them around, do what you like. But when the light comes on you must have produced two groups of coins containing the same number of red side up ones.
I'm very proud of myself in that I figured it out. Can you?