Bifalgorithm post · Brisk · Chapter 1

Are the numbers 18 and 25 congruent modulo 7?

Are the numbers 18 and 25 congruent modulo 7? (Brisk · Chapter 1) — "the numbers 18 and 25 con- gruent mod 7? Yes. If we take groups of 7 out of 18 stones, we’…

Ideas in this flowchart

  • Are 18 and 25 congruent modulo 7?
  • Initial answer: Yes.
  • Taking groups of 7 from 18 gives two groups, totaling 14 stones.
  • There are 4 stones left over from 18.
  • Taking groups of 7 from 25 gives three groups, totaling 21 stones.
  • There are 4 stones left over from 25.
  • Stated conclusion: 18 and 25 are not congruent modulo 7.
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Are the numbers 18 and 25 congruent modulo 7?

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Brisk

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"the numbers 18 and 25 con- gruent mod 7? Yes. If we take groups of 7 out of 18 stones, we’ll get two such groups (a total of 14 stones) and have 4 left over. And then, if we do that same with 25 stones, we’ll get three such groups (a total of 21 stones) and again have 4 left over. So they’re not congruent mod 7."

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