Hello math-fun and SeqFan, I don't know if this is old hat -- if yes please ignore. Rules for a new arrangement of the natural integers : 0) At the beginning there was a (semi)-infinite row of empty labels; 1) Then came the Pencil who wrote "1" on the first (most- left) one; 2) "1" meant: "write now whatever integer you want (but not used so far) on the label to the right of me at a distance of "1" step; [and, more generally, an odd integers means: "go 2k+1 labels to the right and write smthg new on it -- the label must be blank, though". An even integers means: "go 2k labels to the left and write...".] Question: is there an algorithm to rearrange all the na- tural integers with those two simple rules (leaving no empty labels behind) ? I have started this possible sequence (a dot means "still empty label"; the next label to be named has an "x"): 1 3 5 7 2 11 15 4 17 13 9 6 21 23 25 27 10 . . 8 . 12 14 . 17 19 . . . . . . . 20 . . 22 . . 24 . x 18 . 32 . . . . . This sequence looks like an "flat maze" -- thus the name. The above has been done by hand -- this explains why the rows are 10 integers long: labels are easier to reach be- cause a vertical step (downwards) adds 10 to the count. Best, É.