Inside the Loop: The Winding Wall
Read the puzzle
A 12 by 12 dotted grid holds one closed wall. With columns 0 to 12 from the left and rows 0 to 12 from the top, the wall joins these corners in order with straight lines, then returns to the start: (6,0) (8,0) (8,2) (9,2) (9,1) (10,1) (10,5) (9,5) (9,6) (10,6) (10,7) (11,7) (11,8) (10,8) (10,9) (7,9) (7,12) (6,12) (6,11) (5,11) (5,12) (3,12) (3,11) (2,11) (2,10) (3,10) (3,8) (2,8) (2,9) (1,9) (1,8) (0,8) (0,6) (1,6) (1,4) (2,4) (2,3) (3,3) (3,4) (6,4) (6,3) (7,3) (7,1) (6,1). Gems sit at the centres of squares: A (8.5,1.5), B (9.5,5.5), C (6.5,3.5), D (5.5,11.5). Which gem is INSIDE the loop?
Which gem is INSIDE the loop?
Count wall crossings on the way to the edge: odd means inside.
C
Gem C is inside; A, B and D sit in pockets that open to the outside.
How to solve it
Use the crossing rule: from a gem, run a straight line to the edge of the picture and count how often it crosses the wall. Odd means inside, even (including zero) means outside.
Gem A sits in a narrow notch at the top right. A line straight up from A meets no wall, because the top stretch of wall covers only the columns to its left. Zero crossings: outside.
Gem B sits in a notch on the right side. A line straight right from B reaches the edge without touching the wall. Zero: outside.
Gem D sits in a notch on the bottom edge. A line straight down from D crosses nothing. Zero: outside.
Gem C sits just under an inner corner near the top middle. A line straight up from C crosses the wall three times before it reaches the edge. Three is odd, so C is inside.
The usual mistake is to judge by eye: A, B and D look boxed in by wall on three sides, but each pocket opens outward. Takeaway: count crossings, and pick the shortest line to the edge.
Learn the method: How to Solve Loop Puzzles: The Inside and Outside Method
