Using your Head is Permitted

April 2012 riddle

UPDATE (10 April): You may assume that both α1 and α2 are positive.

This is a classic riddle. References will be given on the solution page.

Prove that given irrational α1 and α2 with 1/α1+1/α2=1, the sequences floor(i1) and floor(i2), for i=1,..., partition the naturals. (That is to say that every natural appears in exactly one of the sequences.)

List of solvers:

Hamidreza Bidar (1 April 20:34)
Joseph DeVincentis (4 April 10:13)
Oded Margalit (8 April 02:26)
Adam Daire (11 April 00:50)
Jaesong Lee (11 April 01:09)
Djinn Lu (11 April 16:16)
Albert Stadler (13 April 05:45)
Sylvain Becker (13 April 21:59)
Dan Dima (15 April 19:17)
Ganesh Lakshminarayana (20 April 22:39)

Elegant and original solutions can be submitted to the puzzlemaster at Names of solvers will be posted on this page. Notify if you don't want your name to be mentioned.

The solution will be published at the end of the month.


To solution

Back to main page