Problem 21 · 2013 Math Kangaroo
Stretch
Arithmetic & Operations
sum-constrainttotal-then-divide
Chrissi wants to sell 10 glass marbles that each have a different weight. Their weights are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 dag. They are to be packed into bags, two marbles at a time, so that each bag has the same weight. Which two marbles will be put into the same bag?
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Answer: C — 3 and 8
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Hint 1 of 3
Ten marbles two at a time make 5 bags, and all five bags weigh the same.
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Hint 2 of 3
Add all the weights 1 + 2 + ... + 10 = 55, then share that equally among 5 bags.
Still stuck? Show hint 3 →
Hint 3 of 3
Each bag must weigh 11, so find the marble that pairs with 3 to make 11.
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Approach: equal-sum pairing
- The total weight is 1+2+···+10 = 55, and 5 bags means each weighs 11 dag.
- Pairs making 11: (1,10), (2,9), (3,8), (4,7), (5,6).
- So 3 goes with 8.
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