Inside the Loop: The Trapped Gem
Read the puzzle
A dotted grid has columns 0 to 10 (left to right) and rows 0 to 10 (top to bottom). One closed wall joins these points in order: (7,1) (8,1) (8,2) (9,2) (9,4) (10,4) (10,7) (9,7) (9,10) (8,10) (8,9) (7,9) (7,8) (6,8) (6,10) (5,10) (5,9) (3,9) (3,8) (1,8) (1,7) (2,7) (2,4) (5,4) (5,2) (7,2), then back to (7,1). Four gems sit in squares centred at A (8.5,1.5), B (5.5,2.5), C (7.5,9.5), D (1.5,6.5). Which gem is inside the loop?
Which gem is INSIDE the loop?
Count wall crossings on the way to the edge: odd means inside.
B
Gem B is inside; A, C and D sit in pockets that open to the outside.
How to solve it
Use the crossing test. From a gem, draw a straight line to the edge of the picture and count how many times it crosses the wall. An odd count means inside; an even count, including zero, means outside.
Gem A sits beside the top right notch. A line straight up from A crosses no wall, because the wall passes below A there. Zero crossings: outside.
Gem B sits under the top edge near the middle. A line straight up from B crosses the wall once and then reaches open space. One crossing: inside.
Gem C sits in a pocket at the bottom. A line straight down from C reaches the edge with no crossing. Zero: outside. Gem D sits in a pocket on the left; a line to the left crosses nothing. Zero: outside.
So the trapped gem is B. Many solvers pick C or D because they sit tucked into corners of the wall, but each of those pockets opens to the outside.
Takeaway: one crossing count settles it faster than tracing the whole wall.
Learn the method: How to Solve Loop Puzzles: The Inside and Outside Method
