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If don't want to use algebra, just logical thinking...
  1. The sum of $5 notes needs to end in 0 (not in 5), because the sum of $2 notes can't be end in impair number. => we have even-numbered $5 notes => we have even-numbered $2 notes.
  2. possible variations for a $5 notes (to make it less than 50): A. 2 pieces: $10 B. 4 pieces: $20 C. 6 pieces: $30 D. 8 pieces: $40 E. 10 pieces: $50
  3. Based on the 2nd point => the sum of $2 notes need to end also in 0. => the possible variations: a. 5 pieces: $10 b. 10 pieces:$20 c. 15 pieces: $30 d. 20 pieces: $40 e. 25 pieces: $50
For a total amount of $50, we need:
  • A,d
  • B, c
  • C, b
  • D, a
  • E
  • e Of the above 6 options, only in one case is the total number of banknotes 16 (C, b)
The answer: Harry have 6 pieces of $5 notes.