Question

"a coin purse contains coins with values of 1 cent, 5 cents, 10 cents, 25 cents, and 50 cents. using each coin at least once, what is the minimum number of coins required to equal the highest possible total less than $2?"

Answer 1

11 coins for $1.99

Explanation:

The maximum total less than $2 is $1.99. It takes 11 coins to make that total. It would take 1 fewer if the nickel were not required.

Starting with the minimum required coins, which total $0.91, we need to add $1.08 using a minimum number of coins. To minimize the added coins, we start with the largest we can use without going over the total: 2×50¢ + 1×5¢ + 3×1¢. These 6 coins added to the required 5 coins give the desired total using 11 coins.

11 coins: $1.99 . . . . (3×50¢ +1×25¢ +1×10¢ +2×5¢ +4×1¢)

$1.99 is the highest possible total less than $2.00, and it takes a minimum of 11 coins to make that total.