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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