Friday, October 21st, 2011...9:24 pm

Jay Leno meets Martin Gardner

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It is October 21, 2011 and around the world have been, are, or soon will be Celebration of Mind events to honor Martin Gardner who was born on this day in 1914. His work and writing, which infused fun into math, touched millions of lives. The Celebration of Mind at Davidson College will be in December. To honor Martin Gardner on this day, I present a version of his delightful puzzle “The Missing Dollar from aha! Gotcha. I’ll modernize it a bit and by the end lose much more than a dollar!

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It’s autumn. Crisp air paints the landscape with fiery colors. It is time for football, soccer, and volleyball. Cub Scouts sell popcorn. Driveways become displays of household treasures in yard sales. Suppose your entire block decides to have such yard sale over two days. The participating houses fill a table with vinyl records. The first day, the more standard larger records are sold 2 for $3 and the
smaller 45 records are sold 3 for $3. You sell 30 standard records (totaling $45 income) and 30 of the smaller records (yielding $30 of income) giving a grand total of $75 in record sales. The neighbors look for more records enabling another impressive display of nostalgic turntable tunes to be available on the second day of the yard sale. However, on this day, they decide to sell the records 5 for $6. Amazingly, they sell exactly 60 records, just like the first day! They total their sales and find they made $72 this day! Where is the missing $3?

It’s only $3. Who cares? This time, suppose Jay Leno, known for his large collection of cars, buys eight Rolls Royces at a price of two for $500,000 and eight BMW convertibles at four for $340,000. Jay can close the deal with a $2,680,000 cashier’s check. Before the cars are delivered, Jay has a change of heart. If we use the reasoning from the previous problem, Jay could sell the cars at a price of six for $840,000 or $140,000 each. I’ll take six Rolls Royces, please, which costs me only $840,000 even though they are worth two million dollars according to the original sale. Ah, clever! In that case, I must buy all the cars or no deal. Suppose I do! Now, I only need to pay Jay $2,240,000 for all sixteen cars. That’s a loss of $440,000! Not funny…not funny at all!

Why? Dig around…play with the numbers…and celebrate the way Martin Gardner could captivate minds with math!

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