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The man takes the 5 quart bucket and fills it up. Then he dumps the water into the 3 quart bucket. Then he dumps the 3 quart bucket back in the river. He then dumps what's left in the 5 quart bucket (2 quarts)into the 3 quart bucket. Then he fills up the 5 quart bucket. Both buckets together now total 7 quarts: 5 quarts in the 5 quart bucket and 2 quarts in the 3 quart bucket.
well done
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