Logic Puzzle The Mixed-Up Schedules

Logic Puzzle (HARD!):

The Mixed-Up Schedules

Scenario:
Four friends – David, Miriam, Sarah, and Jacob – each have a different class first period: Math, Science, English, and History. They each make one statement about their schedules:

1. David says, "I have Math first period."
2. Miriam says, "David has Science first period."
3. Sarah says, "Miriam has History first period."
4. Jacob says, "I have English first period."

Only two of these statements are true. Who has which class first period?

Logic Puzzle Answer:

• If David's statement is true (David has Math), then:
  • Miriam's statement (David has Science) is false.
  • Sarah's statement (Miriam has History) could be true or false.
  • Jacob's statement (Jacob has English) could be true or false.
• If Miriam's statement is true (David has Science), then David's statement is false, and we need to check the other statements for two truths:
  • Sarah's statement (Miriam has History) must be false.
  • Jacob's statement (Jacob has English) could be true.

Since only two statements can be true and if David has Math, Jacob could have English, and we need to check Sarah's statement for contradiction:

• If Sarah's statement is true, Miriam has History. Therefore, Sarah and Jacob have conflicting classes for David having Math.

We conclude:

• David has Math (David's statement true).
• Jacob has English (Jacob's statement true).

Therefore:

• Miriam cannot have History (Sarah's statement false).
• David cannot have Science (Miriam's statement false).

Then:

• Miriam has Science.
• Sarah has History.

David – Math, Miriam – Science, Sarah – History, Jacob – English.