# FindShortestTour shows erratic behaviour wrt 2nd argument

FindShortestTour behaves erratically. It should return a {distance, ordering} pair, and it does this for most values of its second argument. But for two cases shown below, it returns an empty list. There is no mention of this possibility in the Mathematica documentation. There is no apparent reason for this behaviour. There are no errors or messages thrown during execution.

places = {{-0.16799965940098155,
0.24175153562415813}, {-0.2486071472529178,
0.20618977684683304}, {-0.14076440088637684, \
-0.24171243009574903}, {-0.6251900796628861, -0.9717675903858705}, \
{-0.17963581832506564, -0.5233794053664629}, {0.266014045257439, \
-0.2574537949317151}, {0.43866600854230675, -0.3502551214679294}, \
{0.8152887752208928, -0.152895668542801}, {0.0849331507331597, \
-0.09587917268794487}};

Array[FindShortestTour[places,#,9]&,8]

If you copy and paste and execute this code, you will see that the 3rd and 6th entries are empty. Why?

• I think it would be a good idea to submit a bug report with this example to Wolfram Support. – Henrik Schumacher Sep 1 '18 at 16:02