Question

A square with four sets of symbols is to be divided into four equal parts such that each part contains all four symbols. Which of the shapes fulfills the condition? 

• A. A
• B. B
• C. C
• D. D

Hint:

For “each part must include all categories,” prefer partition shapes that sample multiple rows and columns symmetrically; avoid corner-heavy footprints like \(L\)-shapes.

Answer 1

The Correct Option is A, B

Step 1: Read the distribution.
The symbols are arranged so that each row and each column contains all four types. Any valid part must therefore cut one of each type across the placement.
Step 2: Test shapes.
(A) The vertical strip can tile the square into four equal strips; because each column already has all four symbols, each strip captures one of each \(⇒\) Valid.
(B) The symmetric \(T\) also tiles the square in four orientations about the center; its footprint spans cells from distinct rows and columns, ensuring one of each symbol in every part \(⇒\) Valid.
(C) The \(L\)-shape over-weights corners; at least one part would repeat a symbol and miss another \(⇒\) Invalid.
(D) The stepped \(T\) similarly fails to sample all rows/columns evenly \(⇒\) Invalid.
\[ \therefore \boxed{(A)\ \text{and}\ (B)}\ \text{fulfill the requirement.} \]