Weighings

weighings are Sufficient to find a bad Coin among Coins. vos Savant (1993)gives an algorithm for finding a bad ball among 12 balls in three weighings (which, in addition, determines if the bad ballis heavier or lighter than the other 11).

Bachet's weights problem asks for the minimum number of weights (which canbe placed in either pan of a two-arm balance) required to weigh any integral number of pounds from 1 to 40. Thesolution is 1, 3, 9, and 27: 1, , 3, , , , , , 9, , ,, , , , , , and so on.

References

Bachet, C. G. Problem 5, Appendix in Problèmes plaisants et délectables, 2nd ed. p. 215, 1624.

Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 50-52, 1987.

Kraitchik, M. Mathematical Recreations. New York: W. W. Norton, pp. 52-55, 1942.

Pappas, T. ``Counterfeit Coin Puzzle.'' The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, p. 181, 1989.

Tartaglia. Book 1, Ch. 16, §32 in Trattato de' numeri e misure, Vol. 2. Venice, 1556.

vos Savant, M. The World's Most Famous Math Problem. New York: St. Martin's Press, pp. 39-42, 1993.

• Dynkin Diagram
• Dürer's Conchoid
• Dürer's Magic Square
• Dürer's Shell Curve
• e
• Ear
• Early Election Results
• Eban Number
• Eberhart's Conjecture
• Eccentric
• Eccentric Angle
• Eccentric Anomaly
• Eccentricity
• Eccentricity (Graph)
• Echidnahedron
• Eckardt Point
• Eckert IV Projection
• Eckert VI Projection
• Economized Rational Approximation
• Eddington Number
• Edge-Coloring
• Edge Connectivity
• Edge (Graph)
• Edge Number
• Edge (Polygon)