QuickenBrain

Turn before combining

Track a quarter-turn of the first pattern, then apply the combining rule.

Keep the two operations separate

AA ↻ 90°BResult
(A ↻ 90°) ∪ B

In this example the rule is: turn A a quarter-turn clockwise, then combine it with unchanged B using union. Follow a corner: top left becomes top right. The top position becomes the right position. Turn the whole first pattern, not each mark in place.

Lesson help

Infer the turn and operation from complete rows or columns. Extended Level 6 turns A before union or difference; Level 7 uses exactly one. Level 8 can turn both patterns.

About this lesson

Try the method in a practice when you are ready.

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Keep the two operations separate

In this example the rule is: turn A a quarter-turn clockwise, then combine it with unchanged B using union. Follow a corner: top left becomes top right. The top position becomes the right position. Turn the whole first pattern, not each mark in place.

AA ↻ 90°BResult
(A ↻ 90°) ∪ B

Turn, then remove the overlap

A is marked at the top left and top. After the clockwise turn, its marks are at the top right and right. B is marked at the top right and bottom. Combining by exactly one removes the shared top-right mark, leaving right and bottom.

After the turnBResult
(A ↻ 90°) ⊕ B

Keep B fixed

A is marked at the top and bottom left. B is marked at the right. Turn A a quarter-turn clockwise, then take A minus B. Work out the turned positions before removing any marks.

AB?Result
(A ↻ 90°) − B

Try it

Which single mark remains?

  1. Top left
  2. Bottom right
Show the answer

Top left

Yes. A turns to right and top left. Removing B’s right mark leaves top left.

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