science

Money

cryotosensei

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.


