Question

The shapes below correspond to different (single-digit) numbers. Choose the option that replaces the question mark.

• A. A
• B. B
• C. C
• D. D

Hint:

When symbols stand for digits, translate each line to algebra and test the smallest consistent two–digit products first.

Answer 1

The Correct Option is B

Let \(\heartsuit=h,\ \spadesuit=s,\ \diamondsuit=d,\ \clubsuit=c\) (all distinct digits). From the first equation, \[ \heartsuit \times \spadesuit=\ \diamondsuit\clubsuit ⇒ h\,s=10d+c. \] From the second, \[ (\diamondsuit\clubsuit)\times \heartsuit=\heartsuit\spadesuit+? ⇒ (10d+c)h=(10h+s)+?. \] Hence \[ ?=(10d+c)h-(10h+s). \] Trying the smallest two–digit products that satisfy the first line gives \[ h=3,\ s=4\ ⇒\ hs=12 \text{ so } d=1,\ c=2. \] Then \[ ?=(12)\times 3-(34)=36-34=\boxed{2}=\clubsuit, \] which matches option (B). Note: Another valid assignment \(h=2,\ s=7\) also satisfies the equations and yields \(?=\diamondsuit\). If the puzzle assumes the smallest consistent digits, the answer is (B).