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www.mikescher.com/www/statics/euler/Euler_Problem-031_explanation.md

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The algorithm here enumerates through every possible combination using an approach similar to counting binary:

  • Increment the last digit until our total sum is greater 200 (test for every combination if total sum == 200)
  • Then set every field from back to front to zero until you find a non-zero field
  • Set this field also to zero
  • Increment the field before ... repeat
  • Abort the loop when you have used every field

That is probably not the most efficient way, but I optimized this brute-force variant enough that it becomes viable.