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Mathematical Fun: Will Some | One Sum

Mathematical Fun: Will Some | One Sum preview
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Look Inside · 7 pages

Will some one sum? puzzle: place digits 1 to 9 in a three-digit addition, counting 9! = 362880 orders and when to carry
Launch problem to open a counting and addition investigation
No-carry case: algebra gives g + h + i = 22.5, and an odd/even parity table confirms the puzzle needs a carry
Proof by contradiction to discuss as a class
Carry from units to tens: answer digits total 18; partitions of 18 into 3 parts filter to 7, giving 42 ordered sums
Guided reasoning on partitions and permutations
Ruling out impossible sums and pairing carry solutions, with 16 colored additions that total 891 and 918 as examples
Check-this-out prompts for students to verify each step
Python permutations code searching all 362880 digit orders finds 336 solutions, including 16 that total 891
Coding extension: test the conjecture by computer search
Summary of solutions: 32 additions for 891 and 918, a table of carry pairs and triples, and a total of 336 ways
Reference for checking student solutions
Appendix of Python output listing solutions for 495, 549 and 837 plus the interesting triple of 954
Optional deeper look for students who want more
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Author
So, what if ... by Ian F Hailes
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About This Product

Will Some | One Sum is a 7-page printable activity full of math puzzles. Students will explore computer coding and Python code.

What's Included

1 PDF with 7 ready to print pages

Resource Tags

math fun math puzzles computer coding number work Python code

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