Using a typical bench DVM, with an input resistance of say 1Mhm: the resistance would still be a nominal 618.2hm:
The fact that someone has taken the trouble to assemble and measure with a meter, which gave 618hm: should convince you its 618hm:, UNLESS you havn't given us the FULL puzzle...
The key to this puzzle is where you start from. I found my notes again and decided to have an other go at it. I hadn't look at this thread so all the newer solutions were unknown to me.
Firstly the connecting leads are at the RHS of the puzzle so the minimum value of the RHS string can never be less than 500hm: It will be the parrallel value of 1khm: in parrallel with (1khm: + Xhm
Then I started working the way through from the LHS of the puzzle by series parralleling the sections of three resistors.