Inside the Loop: Four Gems
Read the puzzle
A board has grid points numbered 0 to 6 across (left to right) and 0 to 6 down (top to bottom). One closed wall joins these points in order: (0,2), (1,2), (1,1), (2,1), (2,2), (4,2), (4,3), (5,3), (5,4), (6,4), (6,6), (3,6), (3,4), (0,4), then back to (0,2). Four gems sit at square centres: B at (0.5,1.5), A at (3.5,2.5), C at (4.5,2.5), D at (2.5,4.5). Which gem is inside the loop?
Which gem is INSIDE the loop?
Trace a straight line from a gem to the edge and count the walls.
A
A line from A to the edge crosses the wall once (odd): A is inside. B, C and D reach the edge without crossing.
How to solve it
Use the crossing count. From a gem, draw a straight line to the edge of the board and count how many times it crosses the wall. An odd count means inside; an even count, including zero, means outside.
Gem A: go straight up. The line meets the top wall that runs from (2,2) to (4,2) once, then reaches the edge. One crossing is odd, so A is inside.
Gem B: go straight left. It reaches the board edge without touching any wall, because the left wall only runs between rows 2 and 4. Zero crossings, so B is outside.
Gem C: go straight up. Nothing is above it; the wall turns down at column 4, just to its left. Zero crossings, outside.
Gem D: go straight down. The bottom wall only spans columns 3 to 6, so nothing is crossed. Outside. Going up instead gives two crossings, which is still even and agrees.
The trap is C, sitting right beside A and looking enclosed. It lies in the notch where the wall steps down, outside the shape. Takeaway: any straight line works, as long as you count every crossing.
Learn the method: How to Solve Loop Puzzles: The Inside and Outside Method
