Glass Overlay: Shared Lines
Read the puzzle
A 3 by 3 grid of cards; each has nine dots numbered 1 to 9 like a keypad (1 top left, 9 bottom right), with lines joining neighbouring dots. Heading: only shared lines stay. Row 3: card 1: 1-2, 2-5, 2-4, 4-7, 7-8, 3-6; card 2: 1-5, 5-9, 2-3, 3-6, 5-6, 4-7; card 3 is missing. Options: A: 3-6, 4-7. B: 1-2, 2-3, 1-5, 2-4, 2-5, 3-6, 5-6, 5-9, 4-7, 7-8. C: 1-5, 3-6, 4-7. D: 1-2, 2-3, 1-5, 2-4, 2-5, 5-6, 5-9, 7-8. Which card completes the grid?
Which card completes the grid?
Keep only the lines that appear on both of the first two cards.
A
In each row, only lines on both cards stay. Row 3 gives card A.
How to solve it
Number the dots 1 to 9 like a keypad. In each row, lay card 1 over card 2 and keep only the lines that appear on both.
Test it on row 1. Card 1 has 1-4, 4-7, 2-4, 3-5, 5-7 and 5-9; card 2 has 2-3, 3-5, 2-4, 4-7, 4-8 and 6-8. The shared lines are 2-4, 3-5 and 4-7, which is the third card.
Row 3: card 1 has 1-2, 2-5, 2-4, 4-7, 7-8, 3-6 and card 2 has 1-5, 5-9, 2-3, 3-6, 5-6, 4-7. Going through card 1's list, only 4-7 (left side, lower half) and 3-6 (right side, upper half) are also on card 2. That is card A.
The traps: B keeps every line from both cards, D keeps the lines found on only one card, and C adds the diagonal 1-5, which is on card 2 only.
Quick check: every line in the answer must be on both cards.
