Problem 8 · Sort into cases and check a limit · 5 points
Made by AI and not reviewed by a real person.
Maja has plenty of 1-cent, 2-cent, and 5-cent coins. In how many different ways can she pay exactly 15 cents using no more than 6 coins? The order of the coins does not matter.
- 5
- 6
- 4
- 2
- 3
Show a hint
- Think about how many 5-cent coins Maja could use. For each possibility, check both the total value and the number of coins.
- Could she reach 15 cents with no 5-cent coins? If she uses two 5-cent coins, how can she make the rest?
Show the answer and solution
Answer: C — 4
With no 5-cent coins, six coins are worth at most 12 cents. With one 5-cent coin, she needs five 2-cent coins. With two 5-cent coins, she can add 2+2+1 or 2+1+1+1. Three 5-cent coins also work. That makes 4 ways. Counting 5+5+1+1+1+1+1 as another way is a trap: it uses 7 coins.