Toothpick Problems





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Hint: Squares can overlap. Be systematic count the squares from smallest to largest or largest to smallest and from top to bottom, left to right or bottom to top, right to left or ... Make a table with the results, find patterns, make a rule, function, equation ...


Make a table with the number of toothpicks and the number of squares. Start with 1x1 and when comfortable with understanding the progression of additional 1x1 squares move on to 2x2, and further.


Size of square Nummber of toothpicks

Number of squares

1 x 1 4 1
2 x 2 12 4
3 x 3 24 9
4 x 4    
5 x 5    


Mind boggler: What are the different ways solutions can be considered and discovered? Try toothpick perimeter and total toothpick pattern



Dr. Robert Sweetland's notes
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