The late Zane C. Hodges proposed this dilemma in his famous desert illustration:

Let me begin with a strange scenario. Try to imagine an unsaved person marooned on a tiny, uninhabited island in the middle of the Pacific Ocean. He has never heard about Christianity in his life. One day a wave washes a fragment of paper up onto the beach. It is wet but still partly readable. On that paper are the words of John 6:43-47. But the only readable portions are: “Jesus, therefore, answered and said to them” (v. 43) and “Most assuredly, I say to you, he who believes in Me has everlasting life” (v. 47). Now suppose that our unsaved man somehow becomes convinced that this person called Jesus can guarantee his eternal future since He promises everlasting life. In other words, he believes Jesus’ words in John 6:47. Is he saved?