Problem 28 · 2013 Math Kangaroo
Stretch
Logic & Word Problems
Counting & Probability
work-backwardcasework
Dad made 6 pancakes one after another and numbered them 1 to 6 in the order he made them. Sometimes while he worked his children ran into the kitchen and ate the hottest pancakes. In which of the following orders could the pancakes not have been eaten?
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Answer: D — 456231
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Hint 1 of 2
Children always grab the hottest available pancake — the most recently made uneaten one.
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Hint 2 of 2
That makes the eating order a stack (last in, first out); test each option for a stack violation.
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Approach: valid stack pop order
- The hottest pancake is the most recently made one not yet eaten, so eating works like popping a stack.
- An eating order is possible only if it is a valid stack-pop sequence of 1,2,3,4,5,6.
- Order 456231 fails: eating 4, 5, 6 first means 1, 2, 3 are still stacked with 3 on top, so the next pancake eaten must be 3, not 2.
- So 456231 could not have happened.
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