Flip, Then Turn
Read the puzzle
A square card shows a 3 by 3 grid of cells, gold (1) or dark (0). Rows, top to bottom: 110, 111, 001. Step 1: flip it over left to right, like a mirror. Step 2: give it a quarter turn clockwise. Which card do you get? A: 110, 111, 001. B: 110, 011, 011. C: 110, 110, 011. D: 011, 110, 110.
Which card do you get?
Do the two steps in order: flip first.
B
Flip left-right first, then a quarter turn clockwise: card B.
How to solve it
Do the steps in the order shown.
Step 1, flip left to right: each row is read backwards. The top row gold, gold, dark becomes dark, gold, gold; the middle row stays all gold; the bottom row dark, dark, gold becomes gold, dark, dark.
Step 2, quarter turn clockwise: each column, read bottom to top, becomes a row. The left column gives gold, gold, dark for the top row. The middle column gives dark, gold, gold for the middle row. The right column gives dark, gold, gold for the bottom row. That is card B.
The common error is turning first and flipping second, which gives card C. With a flip and a turn, the order changes the result. A is the card unchanged, and D is a plain anticlockwise quarter turn with no flip.
Quick check: follow the gold cell in the middle of the top edge. The flip leaves it where it is, and the clockwise turn moves it to the middle of the right edge. B is gold there; C and D are not.
Learn the method: How to Solve Mental Rotation Puzzles: Turned or Mirrored?
