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Seven digits

"I'm thinking of a number. I've squared it. I've squared the square. And I've multiplied the second square by the original number. So I now have a number of seven digits whose final digit is a 7," said Dr. Dingo to his daughter.
Can you work out Dr. Dingo's number?

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Tags: numbers
If you enjoyed this puzzle, check out Sunday Afternoon Maths XVIII,
puzzles about numbers, or a random puzzle.

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