Problem 11 · Pigeonhole principle · 3 points
Made by AI and not reviewed by a real person.
A toy dragonfly has four wings. Tia puts five stickers on its wings, each on exactly one wing; which statement MUST be true?
- Some wing has no stickers.
- Every wing has a sticker.
- Some wing has at least two stickers.
- Exactly one wing has two stickers.
- Some wing has three stickers.
Show a hint
- Think about what “MUST be true” means. Try different ways to spread the stickers among the wings; one possible arrangement can rule out a statement.
- Suppose each wing could hold no more than one sticker. How many stickers could the four wings hold altogether?
Show the answer and solution
Answer: C — Some wing has at least two stickers.
If each wing had no more than one sticker, the four wings could hold at most four stickers. Tia has five, so some wing has at least two stickers. It does not follow that every wing has a sticker: Tia could put all five on one wing, leaving the other three empty.