Problem 17 · 2023 Math Kangaroo
Stretch
Spatial & Visual Reasoning
work-backward
In one move you may take some (or all) of the building blocks from the top of a stack, turn that group upside down, and put it back in the same place (see picture). Goran starts with the stack on the left and wants to end up with all the blocks ordered by size, as shown on the right. What is the smallest number of moves Goran needs?
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Answer: B — 3
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Hint 1 of 3
A move can only lift a group off the top and turn that whole group over, so the bottom blocks stay put unless you lift everything above them.
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Hint 2 of 3
Look at which blocks are already in the right size order and which clumps are reversed or out of place.
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Hint 3 of 3
Try to undo the disorder one reversed clump at a time, counting how few flips can finish the job.
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Approach: find the smallest set of top-flips that reorders the blocks
- A move lifts some blocks off the top, turns that chunk over, and puts it back, so one move can reverse a top group.
- Comparing the starting stack with the target size order shows which groups are out of place.
- Carrying out the reorder with the fewest such flips takes 3 moves.
- The minimum number of moves is B, 3.
Mark:
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