Problem 10 · 2023 Math Kangaroo
Medium
Logic & Word Problems
balance-scalesum-constraint
The six weights of a scale weigh 1 kg, 2 kg, 3 kg, 4 kg, 5 kg and 6 kg. Rosi places five weights on the two scale pans so that they are balanced. The sixth weight is left aside. Which weight is left aside?
Show answer
Answer: A — 1 kg
Show hints
Hint 1 of 2
Add up all six weights first, then notice the five used ones split into two equal piles.
Still stuck? Show hint 2 →
Hint 2 of 2
For the two piles to be equal, the weight left aside must make the rest share out evenly.
Show solution
Approach: the leftover weight must leave an amount you can split into two equal piles
- Count all six weights together: 1 + 2 + 3 + 4 + 5 + 6 = 21 kg.
- The five weights on the scale make two equal piles, so the leftover must leave an amount you can split in half evenly.
- Leaving the 1 kg aside leaves 20 kg, which shares out as 6 + 4 on one pan and 5 + 3 + 2 on the other — both 10 kg — so the leftover weight is 1 kg.
Mark:
· log in to save