The article presents three mathematical puzzles along with their solutions. The first puzzle revolves around identifying numbers that equal the average of their digits, leading to solutions like 1.500 and 2.250. The second puzzle discusses a painted cube divided into mini cubes, where a simplified approach reveals that by removing painted outer cubes, only an 8x8x8 cube remains, totaling 512 unpainted cubes. The final puzzle involves a countdown game strategy that ensures winning by starting from 100 and deducting numbers to aim for a final target, recommending starting at 96 for a guaranteed win. The author encourages reader participation in suggesting new puzzles.
In the first puzzle, the number that equals the average of its digits, which allows for trailing zeros, is noted as 4.5, with four-digit solutions like 1.500 and 2.250.
For the painted cube puzzle, the key to finding the number of mini cubes without paint is to realize that by removing all exterior cubes, an 8x8x8 cube remains, totaling 512.
In the clever countdown puzzle, to guarantee a win when starting at 100, the first move should be to 96, which ensures landing on zero later.
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