Glass Overlay: Busy Cards
Read the puzzle
Nine cards in a 3x3 grid; card dots are numbered 1-9 like a phone keypad. In rows 1 and 2, the third card keeps only lines on both of the first two. Row 3: card 1 has lines 1-2, 2-3, 1-4, 2-5, 5-8, 2-6, 3-5, 5-6; card 2 has 1-2, 1-4, 3-5, 3-6, 5-6, 6-9, 6-8, 8-9. Options: A 1-2, 1-4, 3-5, 5-6, 6-8; B every line of both cards combined; C 2-3, 2-5, 5-8, 3-6, 6-9, 8-9, 2-6, 6-8; D 1-2, 1-4, 3-5, 5-6. Which card completes the grid?
Which card completes the grid?
Keep only the lines that appear on both of the first two cards.
D
In each row, only lines on both cards stay. Row 3 gives card D.
How to solve it
Read the rule from the first two rows. Lay card 2 over card 1 like a sheet of glass: any line drawn on both cards stays, and any line on only one card disappears. That is why each third card looks emptier than the two before it.
Now apply it to row 3, line by line, using the dot numbers 1 to 9. Card 1 has 1-2, 2-3, 1-4, 2-5, 5-8, 2-6, 3-5 and 5-6. Card 2 has 1-2, 1-4, 3-5, 3-6, 5-6, 6-9, 6-8 and 8-9. The lines on both are 1-2, 1-4, 3-5 and 5-6: a corner at the top left, a diagonal from the top-right dot to the centre, and a short line from the centre to the right.
Match that set of four lines against the options. Card D has exactly those four lines and nothing else, so D completes the grid.
The usual slip is choosing B, which is every line from both cards put together, or A, which adds an extra diagonal 6-8 that only card 2 has. Quick check: the answer card can never hold more lines than either of the cards it came from.
