Design a stylish and modern logo for a puzzle game, incorporating interlocking puzzle pieces in a vibrant color palette of blues, greens, and purples. The pieces should be designed with a sleek, minimalist aesthetic, showcasing subtle gradients and shadows to create depth. Include an abstract representation of a brain or mind, subtly integrated within the puzzle design to symbolize problem-solving and cognitive challenge, all set against a clean, white background for a contemporary look.

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Design a stylish and modern logo for a puzzle game, incorporating interlocking puzzle pieces in a vibrant color palette of blues, greens, and purples. The pieces should be designed with a sleek, minimalist aesthetic, showcasing subtle gradients and shadows to create depth. Include an abstract representation of a brain or mind, subtly integrated within the puzzle design to symbolize problem-solving and cognitive challenge, all set against a clean, white background for a contemporary look.