Sources page biographical material

5.U. PIGEONHOLE RECREATIONS
van Etten. 1624. Prob. 89, part II, pp. 131 132 (not in English editions). Two men have same number of hairs. Also: birds & feathers, fish & scales, trees & leaves, flowers or fruit, pages & words -- if there are more pages than words on any page.

E. Fourrey. Op. cit. in 4.A.1, 1899, section 213: Le nombre de cheveux, p. 165. Two Frenchmen have the same number of hairs. "Cette question fut posée et expliquée par Nicole, un des auteurs de la Logique de Port Royal, à la duchesse de Longueville." [This would be c1660.]

The same story is given in a review by T. A. A. Broadbent in MG 25 (No. 264) (May 1941) 128. He refers to MG 11 (Dec 1922) 193, ??NYS. This might be the item reproduced as MG 32 (No. 300) (Jul 1948) 159.

The question whether two trees in a large forest have the same number of leaves is said to have been posed to Emmanuel Kant (1724-1804) when he was a boy. [W. Lietzmann; Riesen und Zwerge im Zahlbereich; 4th ed., Teubner, Leipzig, 1951, pp. 23-24.] Lietzmann says that an oak has about two million leaves and a pine has about ten million needles.

Jackson. Rational Amusement. 1821. Arithmetical Puzzles, no. 9, pp. 2-3 & 53. Two people in the world have the same number of hairs on their head.

Manuel des Sorciers. 1825. Pp. 84-85. ??NX Two men have the same number of hairs, etc.

Gustave Peter Lejeune Dirichlet. Recherches sur les formes quadratiques à coefficients et à indéterminées complexes. (J. reine u. angew. Math. (24 (1842) 291 371) = Math. Werke, (1889 1897), reprinted by Chelsea, 1969, vol. I, pp. 533 618. On pp. 579 580, he uses the principle to find good rational approximations. He doesn't give it a name. In later works he called it the "Schubfach Prinzip".

Illustrated Boy's Own Treasury. 1860. Arithmetical and Geometrical Problems, No. 34, pp. 430 & 434. Hairs on head.

Pearson. 1907. Part II, no. 51, pp. 123 & 201. "If the population of Bristol exceeds by two hundred and thirty seven the number of hairs on the head of any one of its inhabitants, how many of them at least, if none are bald, must have the same number of hairs on their heads?" Solution says 474!

Dudeney. The Paradox Party. Strand Mag. 38 (No. 228) (Dec 1909) 670 676 (= AM, pp. 137 141). Two people have same number of hairs.

Ahrens. A&N, 1918, p. 94. Two Berliners have same number of hairs.

Abraham. 1933. Prob. 43 -- The library, pp. 16 & 25 (12 & 113). All books have different numbers of words and there are more books than words in the largest book. (My copy of the 1933 ed. is a presentation copy inscribed 'For the Athenaeum Library No 43 p 16 R M Abraham Sept 19th 1933'.)

Perelman. FMP. c1935? Socks and gloves. Pp. 277 & 283 284. = FFF, 1957: prob. 25, pp. 41 & 43; 1977, prob. 27, pp. 53 54 & 56. = MCBF, prob. 27, pp. 51 & 54. Picking socks and gloves to get pairs from 10 pairs of brown and 10 pairs of black socks and gloves.

P. Erdös & G. Szekeres. Op. cit. in 5.M. 1935. Any permutation of the first n²   1 integers contains an increasing or a decreasing subsequence of length > n.

P. Erdös, proposer; M. Wachsberger & E. Weiszfeld, M. Charosh, solvers. Problem 3739. AMM 42 (1935) 396 & 44 (1937) 120. n+1 integers from first 2n have one dividing another.

H. Phillips. Question Time. Dent, London, 1937. Prob. 13: Marbles, pp. 7 & 179. 12 black, 8 red & 6 white marbles -- choose enough to get three of the same colour.

The Home Book of Quizzes, Games and Jokes. Op. cit. in 4.B.1, 1941. Pp. 148 149, prob. 6. Blind maid bringing stockings from a drawer of white and black stockings.

I am surprised that the context of picking items does not occur before Perelman, Phillips and Home Book.

Sullivan. Unusual. 1943. Prob. 18: In a dark room. Picking shoes and socks to get pairs.

H. Phillips. News Chronicle "Quiz" No. 3: Natural History. News Chronicle, London, 1946. Pp. 22 & 43. 12 blue, 9 red and 6 green marbles in a bag. Choose enough to have three of one colour and two of another colour.

H. Phillips. News Chronicle "Quiz" No. 4: Current Affairs. News Chronicle, London, 1946. Pp. 17 & 40. 6 yellow, 5 blue and 2 red marbles in a bag. Choose enough to have three of the same colour.

L. Moser, proposer; D. J. Newman, solver. Problem 4300 -- The identity as a product of successive elements. AMM 55 (1948) 369 & 57 (1950) 47. n elements from a group of order n have a a subinterval with product = 1.

Doubleday - 2. 1971.

In the dark, pp. 145-146. How many socks do you have to pick from a drawer of white and black socks to get two pairs (possibly different)?

Lucky dip, pp. 147-148. How many socks do you have to pick from a drawer of with many white and black socks to get nine pairs (possibly different)? Gives the general answer 2n+1 for n pairs. [Many means that the drawer contains more than n pairs.]

Doubleday - 3. 1972. In the dark, pp. 35-36. Four sweaters and 5, 12, 4, 9 socks of the same colours as the sweaters. Lights go out. He can only find two of the sweaters. How many socks must he bring down into the light to be sure of having a pair matching one of the sweaters?