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sledding

Puzzle

Here are the coins:

dollar coin = 1.00
fifty-cent piece = .50
quarter = .25
dime = .10
nickel = .05
penny = .01

The question is, from one to a hundred, how many different numbers of coins can add up to one dollar?

I’ve solved from one to twenty; you can see my answers for 5-20 in the comments. For many numbers, there’ll be more than one solution. For other numbers, there’ll be no solution. For example, 99 coins can’t equal one dollar, because you’d need a two-cent coin.

The low number would be one: a one-dollar coin. The high number would be 100: 100 pennies. But, what are all the combinations between the two extremes?

What is the highest number of coins (besides 100) that can add up to a dollar? (Easy pea-sy!) How early can you incorporate pennies?

Here are 1-4. Answers for 5-20 in the comments.

1 – one silver dollar
2 – two fifty-cent pieces
3 – one fifty-cent piece and two quarters
4- four quarters
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Comments

5-20

5- one fifty-cent piece, one quarter, two dimes, and one nickel
6 – three quarters, two dimes, and one nickel
7 – two quarters and five dimes
8 – two quarters, four dimes, and two nickels
9 – one fifty-cent piece, one quarter, two dimes and five pennies (lowest number with pennies)
10 – ten dimes
11 – one quarter, five dimes, and five nickels
12 – eight dimes and four nickels
13 – seven dimes and six nickels
14 – one quarter, two dimes and eleven nickels
15 – one quarter, one dime and thirteen nickels
16 – four dimes and twelve nickels
17 – three dimes and fourteen nickels
18 – two quarters, two dimes, four nickels, and ten pennies
19 – two quarters, one dime, six nickels and ten pennies
20 – twenty nickels

The high number

would be 96: 95 pennies and one nickel.

This is getting boring, but

21 – one quarter, three dimes, seven nickels, and ten pennies
22 – one fifty-cent piece, one dime, five nickels, and fifteen pennies
23 – two quarters, one dime, five nickels, and fifteen pennies
24 – four dimes, ten nickels, and fifteen pennies
25 – three dimes, twelve nickels, and ten pennies
26 – two dimes, fourteen nickels, and ten pennies
27 – one quarter, one dime, ten nickels, and fifteen pennies
28 – 3 quarters, and twenty-five pennies
29 – one fifty-cent piece, two dimes, one nickel, and twenty-five pennies
30 – two dimes, thirteen nickels, and fifteen pennies

Re: This is getting boring, but

from 21 on you have to include pennies.
sledding

August 2017

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