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2011 Math Kangaroo

Problem 9

Problem 9 · 2011 Math Kangaroo Medium
Number Theory divisioncareful-counting

A chicken farmer packs eggs in boxes of 6 and boxes of 12. What is the smallest number of boxes he needs to pack 66 eggs?

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Answer: B — 6
Show hints
Hint 1 of 2
Use as many big boxes (of 12) as you can first.
Still stuck? Show hint 2 →
Hint 2 of 2
After the big boxes, fill the rest with boxes of 6.
Show solution
Approach: greedy with the larger box
  1. 66 = 12 × 5 + 6, so five boxes of 12 hold 60 eggs and one box of 6 holds the last 6.
  2. That is 5 + 1 = 6 boxes, and no smaller number works, answer B.
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