# A big thing or a small, the winner takes it all

And now a spot of news I was figuring we'd never see: someone beat ``Pay The Rent'' on The Price Is Right --- that is, didn't just beat what I suspect is a version of the Knapsack Problem to place everything in the correct order, but also stuck with it to walk away with \$100,000. This was during a Big Money-themed week, where the top prizes on various games were increased beyond the bounds of reason --- Punch-a-Bunch was played with a \$250,000 top prize for example (it wasn't won), and Three Strikes played for a \$285,716 Ferrari 458 Spider with iPod dock (it also wasn't won; she didn't get any of the digits right, either), and Plinko played for up to \$500,000 (\$1,600 won) --- and this one, at least, paid out. The contestant went on to the Showcase, and won that too (with a bid just \$498 under the right price, so she was within a razor of a double-showcase win), for a total of \$124,017 in prizes that made her, and here's the funny bit, the third-highest winner in Daytime Price history.

I suspected they were making the game easier in the hopes of getting more winners, by increasing the number of winning combinations. This time there was not just the ten distinct winning combinations but the toughest part --- picking a grocery item to go on top, which has to have a price at least more than the sum of any pair of the others --- was given away. The most expensive bit was more than any pair of prizes, so if you got that right you got the game. For that matter, if you just laid the prices in increasing order, you'd win, which I haven't noticed before either.

For the record the prizes were a can of Parmesan cheese (\$4.99), a pack of D-cell batteries (\$12.99), Toothpaste (\$2.79), Mint ice cream (\$5.79), Beauty bar soap stuff (\$1.59), and Rice cakes (\$2.49), and at this point listing all the ways those win gets more exhausting than enlightening. Anyway you know at least one winning combination. The contestant's was to start with the Rice cakes (\$2.49 for the level); then the Beauty bar and Parmesan (\$6.58); then the Toothpaste and the Ice cream (\$8.58); finally the Batteries (\$12.99) and some poor contestant had to play a time-saver game after that. You have to feel sorry for the contestant who has to play ``Switch?'' after something interesting like that starts out the game.

For the record, the range of price prizes has been \$3.90, \$4.80, \$4.70, \$3.10, \$7.90, \$9.40, \$15.50, and now \$11.40. The range in (most generous) levels has been \$3.20, \$2.00, \$2.10, \$1.30, \$7.90, \$9.40, \$15.50, and now \$11.40.

Given the apparent success of the plan to get somebody, anybody to win, I'm curious whether the price ranges are going to snap back to viciously tight again. Ten winning combinations out of (as I make it out) 180 conceivable means that random guessing gives you a 1-in-18 chance of winning, which is almost as good as ``Half Off'' gives you if you're hopeless. If the contestants can reliably guess which is the most pricey item, then there's 30 distinct plausible arrangements, and a one-in-three chance of a \$100,000 payoff is unsustainable.

Trivia: Congress's 1790 authorization to President George Washington, to select the location for the federal city, allowed the district to be any 100 square miles along the Potomac river between the mouth of the ``Eastern Branch'' (the Anacostia River) and Conigogee Creek (now termed Conocheague Creek), near what is now Hagerstown, Maryland. Source: How The States Got Their Shapes, Mark Stein.

Currently Reading: Words From The Map, Isaac Asimov.

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