I found the citation below here
89e:03084 03E20 Swanson, Leonard G. (1-PRLS); Hansen, Rodney T. The equivalence of the multiplication, pigeonhole, induction, and well ordering principles. (English)Internat. J. Math. Ed. Sci. Tech. 19 (1988), no. 1, 129--131.
Informal set-theoretic arguments are given for the equivalence of the principles mentioned in the title, all of which are stated for the natural numbers. The authors work in Zermelo-Fraenkel set theory, but such arguments should be given in a weaker system of set theory or arithmetic in which the principles in question are not theorems. The strength of several forms of the pigeonhole principle was studied by T. von der Twer [Arch. Math. Logik Grundlag. 21 (1981), no. 1-2, 69--76; MR 84e:03072].