By Gyula Katona

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Math. Monthly, 68, 138-154. SCHREIER, ]. (1932): On tournament elimination system. (Polish). Mathesis Polska, 7, 154-160. S. (196o): Problem E 1399. Amer. Math. Monthly, 67, 82. SLUPECKI, ]. , ~' 286--290. of tournaments. Colloq. B. (1947): The counterfeit coin problem. Math. Gaz. 31, 31-39. SOBEL, M. (1960): Group testing to classify efficiently all defectives in a binomial sample. A contribution in Information and Decision Processes, Ed. by Robert E. Machol, McGraw-Hill, 127-161. (1967): Optimal Group Testing.

21, 27-33 (1971): Foundations of Probability. Holden-Day, San Francisco. SANDELIUS, M. (1961): On an optimal search procedure. Amer. Math. Monthly, 68, 138-154. SCHREIER, ]. (1932): On tournament elimination system. (Polish). Mathesis Polska, 7, 154-160. S. (196o): Problem E 1399. Amer. Math. Monthly, 67, 82. SLUPECKI, ]. , ~' 286--290. of tournaments. Colloq. B. (1947): The counterfeit coin problem. Math. Gaz. 31, 31-39. SOBEL, M. (1960): Group testing to classify efficiently all defectives in a binomial sample.

Many authors (Cantor (1964), Shapiro and S~derberg (1963), Erdos and Renyi (1963) have asymptotical results for l(n). Finally, Lindstr~m (1964), (1965), (1966) proved ti. m n -oo l(n)togn n =2 . (•) Baranyai noticed that i t is not true if n ' ::~. , the 4. ••• , probability • Again, subsets are used to test (any subset). p~ xn is defective, x~ is defective with Renyi proposed to choose the subset randomly, with probability;" Is the number of test much larger than in the traditional case? The answer is definitely "no" (Renyi (1962a), (1961a)): Theorem 16 •.