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Topics: Starter  Arithmetic  Place Value  Problem Solving  Puzzles
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See comments above for many different solutions.
Here are some solutions to a similar puzzle from a book published in 1908:
Christmas Present Ideas
Seasonal, mathematicsrelated gifts chosen and recommended by Transum Mathematics
Teacher, do your students have
access to computers? 

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Transum.org/go/?Start=October6
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Use the digits zero to nine to make the first ten digits (one at a time!)
Here are the solutions to the extension challenge as published in 'A ScrapBook of Elementary Mathematics' in 1908: