Problem 14 · 2015 Math Kangaroo
Stretch
Logic & Word Problems
sum-constraintcasework
In Field Street there are 9 houses in a row. At least one person lives in each house. Each pair of neighbouring houses has at most 6 inhabitants. What is the maximum number of people living in Field Street?
Show answer
Answer: D — 29
Show hints
Hint 1 of 2
To pack in as many people as possible, alternate crowded and nearly-empty houses.
Still stuck? Show hint 2 →
Hint 2 of 2
Try 5, 1, 5, 1, … : each neighbouring pair then totals exactly 6, the most allowed.
Show solution
Approach: alternate large and small to push every adjacent pair to the limit
- Each neighbouring pair may hold at most 6 people, and every house needs at least 1.
- Alternating 5 and 1 keeps every pair at 5 + 1 = 6, the maximum, and uses the minimum (1) in the small houses.
- With 9 houses this is 5, 1, 5, 1, 5, 1, 5, 1, 5 = five 5's and four 1's = 25 + 4 = 29 people.
Mark:
· log in to save