Number Riddle

Number Theory Level pending

Miss Kate wants to test the mathematical skills of Jake and James. She sets up an integer x for them to guess and gives hints separately to both of them. Both of them are told that:

  • 20<x<51
  • x = a(mod b) and x=c(mod d)
  • Both b and d are different primes larger than 20
  • a and c are non-negative integers with a < b and c < d
  • Only Jake is told the value of a and b, and only James is told the value of c and d.

She then sets up a meeting for them, but they aren't allowed to tell the others the values of a, b, c, or d. This is what they say:

  • Jake: I don't know the number yet
  • James: I don't know the number either
  • Jake: Now I know the number
  • James: I still don't know the number

What is the value of c?


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