Problem 11 · 2024 Math Kangaroo
Medium
Logic & Word Problems
work-backwardcareful-counting
The wizard Adam built the tower on the right out of 8 discs. He magically makes discs vanish one at a time. First the 2nd disc from the bottom. Then, counting from the bottom of the new (shorter) tower, the 3rd disc. Then the 4th disc from the bottom of that newer tower. Finally the 5th disc from the bottom of the tower he now has. Which tower is left at the end? (The answer choices are the five pictured towers.)
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Answer: B
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Hint 1 of 2
Number the discs from the bottom and remove them one at a time, re-counting from the bottom after each removal.
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Hint 2 of 2
After each disc vanishes the tower is shorter, so 'third from the bottom' refers to the new, shorter tower.
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Approach: simulate the removals from the bottom step by step
- Bottom-to-top the discs are dark, white, light, dark, white, light, dark, light.
- Remove the 2nd from the bottom (white): dark, light, dark, white, light, dark, light.
- Remove the new 3rd (dark), then 4th (light), then 5th (light) in turn.
- What is left, bottom-to-top, is dark, light, white, dark — tower B.
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