The earliest mention so far discovered of the trick of making two wooden matches penetrate each other is in a booklet by William Robinson, A Few of Robinson's New Ideas, in which the match penetration is shown as a catalogue item, available for purchase, 50¢. The booklet is undated, but is probably from 1898 or earlier, before Robinson assumed his Chung Ling Soo persona.
The earliest explanation for the trick found to date is in the June 9, 1901, issue of The Sunday Chicago Tribune Magazine, n.p. The story tells of four men sitting at a restaurant, exchanging match tricks and puzzles, most all of which have long been grist for beginning texts of magic. Here we are told:
“[A waiter] took a match between the thumb and forefinger of each hand, the matches being interlocked so that it did not seem possible to pull the hands apart without dropping the match from one hand. The waiter said that by long practice he had learned to pull one match right through the other. He pulled his hands quickly apart and gave the appearance of doing as he had said.
“The explanation was that each match, being held tightly in the fingers, stuck tight to the flesh at its phosphorous end. By a quick motion he would open the forefinger or thumb of one hand, making room to permit of the other match being drawn straight out. The match which was raised to permit of the escape of the other one did not drop to the floor because it was held by the phosphorous head to the flesh of the forefinger, and immediately after the other match was drawn out the thumb was jerked back so as to again grasp the end of the match that for a brief part of a second had swung free.”
The earliest written description in conjuring literature seems to be “The Penetrable Match” in Magic, Vol. 10 No. 9, June 1910, p. 66. Ellis Stanyon states no provenance for the trick.
Walter Gibson did credible early write-ups in The Magic World, Vol. 4 No. 9, Dec. 1920, p. 121, and in The Sphinx, Vol. 18 No. 8, Oct. 1919, p. 192, Vol. 18 No. 9, Nov. 1919 p. 215 and Vol. 20 No. 2, Apr. 1921, p. 71. In these he includes various ways of clipping the matches.
The trick has been mistakenly credited to Martin Gardner (despite Gardner's disavowal of any such attribution) and to Boris Zola (see the claim made in Genii, Vol. 12 No. 4, Dec. 1947, p. 99).