Problem 7 · 2016 Math Kangaroo
Medium
Counting & Probability
caseworkspatial-reasoning
A hen lays white and brown eggs. Lisa takes six of them and puts them in a box as shown. The brown eggs are not allowed to touch each other. What is the largest number of brown eggs Lisa can put in the box?
Show answer
Answer: C — 3
Show hints
Hint 1 of 2
Two round eggs touch only when their cups are right next to each other (side by side or one above the other).
Still stuck? Show hint 2 →
Hint 2 of 2
Try putting brown eggs in cups that skip a space, like a checkerboard pattern.
Show solution
Approach: spread the brown eggs out so none are next to each other
- The box has 6 cups in 2 rows of 3. Eggs touch only when their cups are side by side or one directly above the other.
- Put brown eggs in the two top corners and the middle cup of the bottom row — none of these three cups touch.
- A fourth brown egg would have to sit next to one of them, so the most Lisa can place is 3.
Mark:
· log in to save