Problem 23 · 2020 Math Kangaroo
Stretch
Logic & Word Problems
caseworkwork-backward
A panel has 4 circles. When Lucy touches a circle, that circle and every circle touching it switch colour (white ↔ black), as shown. Starting with all circles white, at least how many circles must Lucy touch, one after another, to make all four black?
Show answer
Answer: C — 4
Show hints
Hint 1 of 2
Touching a circle flips it and its neighbours; each circle must end flipped an odd number of times.
Still stuck? Show hint 2 →
Hint 2 of 2
Find the smallest set of touches making every circle's flip-count odd.
Show solution
Approach: make every circle flip an odd number of times
- Touching a circle toggles it and its neighbours; all four start white and must end black (odd flips each).
- One or two touches cannot make all four flip an odd number of times.
- The fewest touches achieving this is 4 (touching each circle once works).
Mark:
· log in to save