PASADENA, CAâSequestered in a private booth at a Pasadena-area Cheesecake Factory for nearly 25 minutes, a party of eight California Institute Of Technology physicists emerged exhausted but visibly excited Friday evening after successfully splitting the bill.

"This is an important day for us, not only because it marks Professor [Wayne] Newbury's birthday, but because we have accomplished a feat thought unimaginable ever since [late computational physicist Philip] Eisenreich found that it was impossible to calculate how a group of paired bodies, set in motion by the presence of a solid-state check, could come to rest at a non-variable, evenly distributed mathematical constant," said lead party organizer and theoretical physicist Dr. Cynthia Dreyfuss.

Before the arrival of the check, several early bill-splitting theories were proposed, including a simple process of dividing it into eight identical fragments, the Random Contribution Model, and a theory posited by Newbury himselfâwho insisted that he was bound to treat everyoneâwhich was widely rejected on the basis that it would undermine the whole objective of the evening.

"When the check came, we all immediately agreed that the total of $284.57 could be defined as an irrational number of dollars for a party of eight to spend at a chain restaurant," said Dreyfuss.

The team of physicists decided to test Dreyfuss's Pay For What You Ordered Algorithm, which hypothesized that it was possible to determine what each individual owed by defining variables such as the cost of one's entrĂŠe, the total number of beverages one consumed, one's percentage of the sum ingestion of the component parts of the Firecracker Salmon Rolls and Buffalo Blasts, and "six bucks toward the birthday boy's meal."

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The process, however, was hindered by Heisenberg's uncertainty principle, as group members failed to document how many drinks they ordered, and those sitting in the vicinity of graduate student in particle physics Susan Politzer suspected that she deliberately falsified her findings regarding the resonant frequency with which she consumed the $7.95 El Diablo margaritas.

"According to the Distribution Of Wine Theory, everyone should chip in $5 to pay for it," gravitational-wave specialist Arjun Patel said. "But after careful observation, the theory falls apart: the bottle never moved from the other end of the table, and Tom Steinbaum was clearly seen staggering in a non-uniform circular motion whenever he got up to use the bathroom."

As the bill approached absolute zero, the scientists found that the closer they got to completely breaking it down, the more difficult it was to calculate.

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"When we kept coming up short by $15, we thought the solution might lie in a damped simple harmonic oscillator, so we mapped complex modes of vibration in diatomic molecules, found the zero-point vibration of the n=0 ground state, studied the motion of atoms in a solid lattice, and formulated the theory of heat capacity," Patel said. "Turns out we were on the wrong track, but it was helpful to know what definitely didn't work."

"Then we remembered to factor in Kiminiski's Constant," Patel added, referring to the integer named after planetary-physics professor David Kiminiski, who departed before the check came but left a $20 bill.

While determining the tip would normally have been dictated by the Law Of Gratuity, which holds the sometimes volatile figure steady at 18 percent, factions within the group nonetheless argued over two competing theories for dealing with the problem: standard variations, and the newer 20 Percent Courtesy Hypothesis.

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"Taking into consideration the fact that [mathematical physicist] Hideo [Akuri]'s Cajun Chicken Littles were primarily made up of dark matter, the waitress's low kinetic energy, above-average mass, and weak attractive force, we devised a formula in which we moved the subtotal's decimal point one place to the left," Dreyfuss said.

The group celebrated by making plans to all go out to Charlie's Steakhouse next weekend in an attempt to find the largest prime rib.