TITLE: English name and references for a combinatorial puzzle from Japan
QUESTION [15 upvotes]: I am looking for the name and references of the following puzzle.
There are n intersecting circles in a row.
At the center of the circle and at the intersection of the two circles, fill the numbers 1, 2, 3, ..., 2n-1.
The number at the intersection should be the sum of the numbers at adjacent two centers.
An example for n=2:

An example for n=3:

The case for n=4:

(A,B,C,...,G) is a permutation of (1,2,3,...,7) satisfying A+C=B, C+E=D, E+G=F.
This puzzle is called "連環の数" in Japanese language.
(Pronunciation is "ren-kan-no-kazu". "ren" means "linked". "kan" means "circle" or "ring". "no" means "of" etc. "kazu" means "number".)
I asked the site owner who uses this Japanese name, but he said he did not know any references and English name.
I would like to discuss or to publish a certain combinatorial property of this puzzle in English, but I am having trouble finding the name and references.
Thank you for reading.
PostScript: Unfortunately, it was determined to be off-topic. Can I repost the same question on puzzling.SE?

REPLY [8 votes]: Tsuyoshi Uema refers to it as a "renkan" puzzle, and has written some code to solve small instances at http://prolog.web.fc2.com/src_017_renkan.html