Turn, Flip, Turn
Read the puzzle
A square card shows a 3 by 3 grid of cells, gold (1) or dark (0). Rows, top to bottom: 101, 011, 010. Step 1: quarter turn clockwise. Step 2: flip over top to bottom. Step 3: quarter turn clockwise. Which card do you get? A: 010, 011, 101. B: 101, 110, 010. C: 010, 110, 101. D: 101, 011, 010.
Which card do you get?
Mark one corner of the card and follow it through each step.
A
Turn, flip top-bottom, turn: the same as one top-bottom flip. A.
How to solve it
Do the three steps in order, or spot the shortcut.
Step 1, quarter turn clockwise (each column read bottom to top becomes a row): the rows become dark, dark, gold; gold, gold, dark; dark, gold, gold.
Step 2, flip top to bottom (the top row becomes the bottom row): dark, gold, gold; gold, gold, dark; dark, dark, gold.
Step 3, quarter turn clockwise again: the top row is dark, gold, dark; the middle row is dark, gold, gold; the bottom row is gold, dark, gold. That is card A.
Shortcut: a turn, a top-to-bottom flip and the same turn again add up to a single top-to-bottom flip, so you can simply swap the top and bottom rows of the starting card.
The usual trap is C, which is a half turn: what you get by doing both turns and forgetting the flip. D is the card unchanged and B is a left-to-right flip.
Quick check: mark the gold cell at the bottom centre and follow it. It ends at the top centre, as in A.
Learn the method: How to Solve Mental Rotation Puzzles: Turned or Mirrored?
