Let's solve this puzzle step by step.
We know that three coins in total add up to 51 cents. Let's assume the three coins are x, y, and z.
Since one of the coins is not a quarter, we can eliminate the possibility of having three quarters because that would exceed 51 cents.
Let's consider the options for the non-quarter coin: penny (1 cent), nickel (5 cents), or dime (10 cents).
a. If the non-quarter coin is a penny, its value would be 1 cent. Therefore, the remaining two coins (x and y) must add up to 50 cents. However, there is no combination of two coins that can add up to 50 cents using pennies, nickels, or dimes. So this possibility can be ruled out.
b. If the non-quarter coin is a nickel, its value would be 5 cents. This means the remaining two coins (x and y) must add up to 46 cents. Possible combinations of coins that add up to 46 cents are:
- 1 quarter (25 cents), 1 dime (10 cents), and 1 nickel (5 cents).
- 2 dimes (20 cents) and 6 pennies (6 cents). Either of these combinations satisfies the condition, so we have two possible solutions:
- Quarter (25 cents), dime (10 cents), and nickel (5 cents).
- Dime (10 cents), dime (10 cents), and 6 pennies (6 cents).
c. If the non-quarter coin is a dime, its value would be 10 cents. This means the remaining two coins (x and y) must add up to 41 cents. Possible combinations of coins that add up to 41 cents are:
- 1 quarter (25 cents), 1 dime (10 cents), and 6 pennies (6 cents).
- 2 dimes (20 cents) and 1 nickel (5 cents). Either of these combinations satisfies the condition, so we have two possible solutions:
- Quarter (25 cents), dime (10 cents), and 6 pennies (6 cents).
- Dime (10 cents), dime (10 cents), and nickel (5 cents).
To summarize, the three possible solutions are:
- Quarter (25 cents), dime (10 cents), and nickel (5 cents).
- Dime (10 cents), dime (10 cents), and 6 pennies (6 cents).
- Quarter (25 cents), dime (10 cents), and 6 pennies (6 cents).