Sources page biographical material

5.S.1. USING CHAIN LINKS TO PAY FOR A ROOM
The landlord agrees to accept one link per day and the owner wants to minimise the number of links he has to cut. The solution depends on whether the chain is closed in a cycle or open at the ends. Some weighing problems in 7.L.2.c and 7.L.3 are phrased in terms of making daily payment, but these are like having the chain already in pieces. See the Fibonacci in 7.L.2.c.

New section. I recall that there are older versions.

Rupert T. Gould. The Stargazer Talks. Geoffrey Bles, London, 1944. A Few Puzzles -- write up of a BBC talk on 10 Jan 1939, pp. 106-113. 63 link chain with three cuts. On p. 106, he says he believes it is quite modern -- he first heard it in 1935. On p. 113, he adds a postscript that he now believes it first appeared in John O'London's Weekly (16 Mar 1935) ??NYS.

Anonymous. Problems drive, 1958. Eureka 21 (Oct 1958) 14-16 & 30. No. 3. Man has closed chain of 182 links and wants to stay 182 days. What is the minimum number of links to be opened?

Birtwistle. Math. Puzzles & Perplexities. 1971. Pp. 13-16. Begins with seven link open-ended bracelet. Then how big a bracelet can be dealt with using only two cuts? Gets 23. Then does general case, getting n + (n+1)(2ⁿ⁺¹ - 1).

Angela Fox Dunn. Second Book of Mathematical Bafflers. Dover, 1983. Selected from Litton's Problematical Recreations, which appeared in 1959 1971. Prob. 26, pp. 28 & 176. 23 link case.

Howson. Op. cit. in 5.R.4. 1988. Prob. 30. Says a 23 link chain need only be cut twice, giving lengths 1, 1, 3, 6, 12, which make all values up to 23. Asks for three cuts in a 63 link chain and the maximum length chain one can deal with in n cuts.