Problem 12 · Parity · 4 points
Made by AI and not reviewed by a real person.
Eight firefly lanterns are off. Each spell flips exactly three different lanterns (on becomes off and off becomes on); after exactly three spells, what is the greatest number that can be on?
- 7
- 8
- 5
- 3
- 6
Show a hint
- Think about whether the number of lit lanterns is odd or even.
- Can one lantern be flipped twice?
Show the answer and solution
Answer: A — 7
Each spell changes the number of lit lanterns from even to odd or from odd to even. Starting at 0, the number lit after three spells must be odd, so 8 is impossible. To get 7, flip lanterns 1, 2, 3; then 4, 5, 6; then 1, 7, 8. Lantern 1 is off again, and the other seven are on. Thus 7 is the greatest possible.