A group of 50 white collar corrupt mathematicians (corrupt accountants, sleazy statisticians, etc) arrive together in a special prison. They aren't told how long they'll be there, but they're told how to get out.

On the day of their arrival, each mathematicians has a colored spot tattooed in the middle of his back. The tattoo is either black or red. He isn't told which color he has, but he is told that all 100 prisoners have such a spot and that they aren't all the same color.

He's then put in an isolated room, where he will spend the rest of his prison term in solitary confinement.

One wall of the room contains 99 recessed video monitors and the opposite wall a small video camera. On the morning of the last day of each year served, these will become active. Each prisoner will strip to the waist in front of the camera and face the video screens, where he will find displayed the bare backs of the other 99 prisoners. He's given 1 minute to note the colors of the spots on the backs displayed. The cameras then become inactive and the screens go dark for another year.

His task then is to determine the color of his own spot using pure logic. Once he knows for a fact what his color is, he informs the warden and is released from prison that very day.

At the end of the following year served, the monitor screens of any prisoners released the previous year will be blank. Release is the only reason a screen will appear blank.

Cheating of any kind, which includes being wrong, acting stupidly, making wild or educated guesses, and facing or hand signaling into the video camera, is punished gruesomely by a long and painful treatment; so it's simply not done.

Assume that all the prisoners have the goal of getting out of prison as soon as possible.

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