Problem 9 · 2010 Math Kangaroo
Medium
Spatial & Visual Reasoning
spatial-reasoning
In the box are seven blocks. It is possible to slide the blocks around so that another block can be added to the box. What is the minimum number of blocks that must be moved?
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Answer: B — 3
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Hint 1 of 2
You need to clear enough room for one more block of the empty shape.
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Hint 2 of 2
Find the fewest blocks to relocate so the free space lines up into one block-sized gap.
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Approach: rearrange to open one block-sized gap
- The seven blocks leave scattered free space; an eighth block fits only after the gaps are merged.
- Sliding 3 blocks is enough to gather the free area into one block-shaped opening, and fewer cannot.
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