Problem 24 · 2023 Math Kangaroo
Stretch
Logic & Word Problems
caseworkwork-backward
Maria colours exactly 5 cells of this grid in grey. Then she has her 5 friends guess which cells she has coloured in, and their answers are the five patterns A, B, C, D and E. Maria looks at the patterns and says: „One of you is right. The others have each guessed exactly four cells correctly.“ Which pattern did Maria paint? (Choose from pictures A–E.)
Show answer
Answer: E
Show hints
Hint 1 of 2
Each friend's guess is a set of 5 cells; one matches all 5, the others match exactly 4.
Still stuck? Show hint 2 →
Hint 2 of 2
Find the pattern that differs from each of the four near-miss guesses in just one cell.
Show solution
Approach: find the true pattern consistent with one exact and four near-misses
- The correct answer shares all 5 cells with one guess and exactly 4 cells with each of the other four.
- So Maria's pattern must overlap four of the diagrams in 4 cells and one in all 5.
- The only pattern fitting every condition is E.
Mark:
· log in to save