January 2019 - Math Problem

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
​C4
​D8

 

AmountBags
​$1​A
​$2​B
​$3A, B
​$4C
​$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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