Problem 10 · 2014 Math Kangaroo
Medium
Logic & Word Problems
careful-counting
Seven sticks lay on top of each other. Stick 2 lays right at the bottom. Stick 6 lays right on top. Which stick lays exactly in the middle?
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Answer: B — 3
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Hint 1 of 3
Where two sticks cross, the one you can see all of is on top and the one that gets hidden is underneath.
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Hint 2 of 3
Build the pile order from the bottom stick (2) up to the top stick (6) by checking each crossing.
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Hint 3 of 3
With seven sticks in a pile, the exact middle one is the 4th counting from the bottom.
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Approach: read each crossing to stack the sticks from bottom to top, then take the 4th one
- At every place two sticks cross, the unbroken stick is the one lying on top.
- Using that, build the order of the pile from stick 2 at the very bottom up to stick 6 at the very top.
- Seven sticks make a pile, and the middle of seven is the 4th one from the bottom.
- That 4th, middle stick is stick 3.
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