Making change for a dollar is a classic problem that can be approached in various ways. Here, we’ll explore the different combinations of coins that add up to 100 cents (1 dollar).
Understanding the Coins
In the United States, the coins commonly used are:
- Penny (1 cent)
- Nickel (5 cents)
- Dime (10 cents)
- Quarter (25 cents)
- Half-dollar (50 cents)
- Dollar coin (100 cents)
Calculating the Combinations
To determine the number of ways to make change for a dollar, we consider all possible combinations of these coins that sum up to 100 cents. This involves using different quantities of each coin.
Total Number of Ways
After considering all possible combinations, it turns out there are 293 ways to make change for a dollar using the standard U.S. coins.
Example Combinations
Here are a few examples of how you can make change for a dollar:
- 100 pennies
- 20 nickels
- 10 dimes
- 4 quarters
- 1 half-dollar and 2 quarters
- 1 dollar coin
These are just a few of the many possible combinations. The total number of ways to make change for a dollar is 293, considering all possible combinations of pennies, nickels, dimes, quarters, half-dollars, and dollar coins.