Every Second Turn

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Every Second Turn Example.png Every Second Turn Example Solution.png

Draw a single, non-intersecting loop that passes orthogonally through all cells, going straight through some cells and turning in others. The cells in which the loop turns must alternate between cells with white circles and cells without white circles. The loop cannot go straight through white circles.

(Rules and example from PGP IB)

Rule Variations[edit]

  • Instead of "every second" rule, "every N-th" rule also works where N is an arbitrary number. If N=1, this puzzle becomes Dutch Loop.
  • In Nth Breakpoint from WPC 2017/Round 13, solvers had to determine the number of turns between consecutive circles.
  • Instead of rules about drawing a loop, rules about drawing a path also works.

History of the Puzzle[edit]

Appeared on WPC 1999/Part 5, an "innovatives" round. The author is unknown. The puzzle is known as "Minden Második Töréspont" in Hungarian that has roughly the same meaning as the English title.

Also called Every Second Breakpoints.


Multi ESB[edit]

Multi ESB Example.png Multi ESB Example Solution.png

First appeared on the first LMI Screen Test contest in December 2010.[1] The puzzle was by Deb Mohanty (India).

Draw several closed loops in the grid passing through centres of cells horizontally and vertically, so that each cell is visited by exactly one loop. The loops must turn at breakpoints, i.e., cells with circles. Additionally, for each loop, there must be exactly one turn between two breakpoints that the loop visits. A loop cannot cross or overlap other loops.

Appearances in the past WPCs[edit]