riddle of the day

Ships keep leaving toward you throughout your seven-day journey. The difficulty is remembering the seven ships that left B during the previous seven days.

The Noon Crossing

Reasoner
Pure logic

Riddle statement

Two ports, A and B, are connected by a shipping route.

Every day, exactly at noon:

  • one ship leaves A for B;
  • another ship leaves B for A.

Every journey takes exactly 7 days.

Today at noon, you board the ship leaving A.

Including ships you meet at the exact moment you leave or arrive, how many ships traveling in the opposite direction will you meet during the crossing?

Show solution

Solution

Call the noon when you leave A day 0.

You will meet every ship that leaves B from day −7 through day 7, inclusive.

  • The day −7 ship reaches A just as you leave.
  • The ships from days −6 through −1 are already at sea.
  • The day 0 ship leaves B at the same moment you leave A.
  • The ships from days 1 through 6 leave during your journey.
  • The day 7 ship leaves B just as you reach B.

These are fifteen consecutive departure dates:

7 earlier ships + 1 ship on day 0 + 7 later ships = 15.