Luke’s has seven coins. He can make 11p with two of his coins. He can make 11p with three of his coins. He can make 11p with four of his coins. What are the seven coin that Luke’s has?

Answer

Luke has a 5p, three 2p coins, and three 1p coins.

Q: How much is each coin worth? A: We do not know.
Q: What range of values can each coin have? A: Each coin must be less than or equal to 11p.
Q: How can we use this information to determine the seven coins that Luke has? A: We can use trial and error.
Q: What two coins can Luke use to make 11p? A: We do not know.
Q: What three coins can Luke use to make 11p? A: We do not know.
Q: What four coins can Luke use to make 11p? A: We do not know.
Q: Are there any combinations of coins that can make 11p that have not already been listed? A: No.