In Regards to the "red marbles, blue marbles" Sorry if this is a repeat, but there is an even better way than the one described, giving you a 100% chance of drawing a red marble.  The hint is in the phrase "you can arrange the marbles however you like". The solution is easy:  put 25 blue marbles on the bottom, and 25 red marbles on the top.  You are assured you will get a red one this way. If you are concerned about them being shaken, try this: Put one red marble in one jar, 50 blue marbles on the bottom of the second jar, and 49 red marbles on top of them.  Unless the jars are inverted while shaking, the chances of the marbles intermingling to the point that it affects your accuracy is minimal. Then again, if you want to get creative, there is nothing in the stated rules that says you can't put something BESIDES marbles in the jar.  Put a cup large enough to hold 25 marbles inside each jar and fill each with red marbles.  Surround the cup with blue marbles.  Although some would say this is cheating, it is not specifically prohibited in the rules of the puzzle. Adam Thayer Wednesday, April 23, 2003   Fog Creek Home