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
​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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