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Fair Fare

Columnist Marilyn vos Savant is famous for her takes on the Monty Hall problem and Wiles' solution of Fermat's Last Theorem. Her original fame is due to the fact that in 1985, the Guinness Book of World Records listed her as having the "World's Highest IQ" at 228...she lost this record in 1989.

In her Sunday columns and books, Marilyn vos Savant does pose some interesting problems. Such as....

Problem: My three girlfriends and I celebrate our birthdays by going out to lunch. The celebrant's lunch is split among the other three friends. We could not get together for a September birthday, so we combined it with another in November. To be fair, how should we split the bill?

Source: "AskMarilyn," Parade, January 17, 2010, p. 22

Hint: Suppose that the bill was \$60 and that normally everyone would pay their fair share of \$15...but now...Share your reasoning with others...expect to not agree!

Solution Commentary: After being involved in multiple discussions regarding this problem, with little consensus as to the right answer...I will merely supply vos Savant's solution (which I disagree with!)....

"Each of the celebrants should pay 1/12th, and the other two friends should pay 5/12ths of the bill.

Here's an illustration. Say that everyone spends \$15, and the bill totals \$60, tax and tip included. The September celebrant owes nothing for her own lunch, but she pays \$5 for one-third of the November friend's lunch. The same for the November celebrant. She pays \$5 for one-third of the September friend's lunch. Each remaining friend owes \$25. This represents the cost of her own lunch (\$15) plus one-third of the cost of each birthday girl's lunch.