You have 15 Loonies (one dollar coins) and four small bags. How many coins would you put into each bag so that you can pay any amount from $1 to $15 without opening bags?
Solution:
| Bag | Number of Coins |
|---|---|
| A | 1 |
| B | 2 |
| C | 4 |
| D | 8 |
| Amount | Bags |
|---|---|
| $1 | A |
| $2 | B |
| $3 | A, B |
| $4 | C |
| $5 | A, C |
| $6 | B, C |
| $7 | A, B, C |
| $8 | D |
| $9 | A, D |
| $10 | B, D |
| $11 | A, B, D |
| $12 | C, D |
| $13 | A, C, D |
| $14 | B, C, D |
| $15 | A, B, C, D |
What if you had 31 coins and 5 bags? How many coins would you put into each bag so that you can pay any amount from $1 to $31 without opening the bags?
How many bags would you use if you had 127 coins and you wanted to pay any amount from $1 to $127?
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