Digit puzzle
Four cards each showed a different digit, one of which was zero. Victor formed the largest four-digit number from the cards, and Martin formed the smallest four-digit number. Adam wrote the difference between Victor's and Martin's numbers on the board.
Then Victor formed the largest possible three-digit number and Martin the smallest possible three-digit number. Adam again wrote the difference between Victor's and Martin's numbers on the board. Then Victor and Martin similarly formed two-digit numbers, and Adam wrote down the difference on the board.
Finally, Victor chose the largest possible single-digit number and Martin the smallest non-zero single-digit number, and Adam wrote down their difference.
When Adam added up all four differences on the board, the total was 9,090. Identify the four digits on the cards.
Then Victor formed the largest possible three-digit number and Martin the smallest possible three-digit number. Adam again wrote the difference between Victor's and Martin's numbers on the board. Then Victor and Martin similarly formed two-digit numbers, and Adam wrote down the difference on the board.
Finally, Victor chose the largest possible single-digit number and Martin the smallest non-zero single-digit number, and Adam wrote down their difference.
When Adam added up all four differences on the board, the total was 9,090. Identify the four digits on the cards.
Final Answer:
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basic operations and conceptsnumbersthemes, topicsGrade of the word problem
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