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Across the Round Table (illustration)
FILE No.75Unsolved

Across the Round Table

Difficulty ★☆☆about 3 minLogic PuzzleRound tableOpposite seats
Seats are numbered around a round table. Seat 3 is directly opposite seat 8. How many seats?

Case Record

A meeting room has a round table with seats numbered 1, 2, 3, ... clockwise at equal spacing. The total number of seats is unknown.

All we know: seat 3 is directly opposite seat 8.

Your question

How many seats does the table have?

Case Files

Evidence

Diagram

Difference = half a turnSeatNumberThis seat3Opposite8Difference8 - 3 = 5 seatsFive seats is half the table.
Diagram

Timeline

  1. The seating plan matters.

Hints

If you get stuck, open the hints one at a time, in order.

Open hint 1

What fraction of the way around is the opposite seat?

Open hint 2

How many steps clockwise is it from seat 3 to seat 8?

Open hint 3

Double it.

Solve It

Your question

How many seats does the table have?

Choose the answer closest to the truth.

Share: I'm solving this

The Truth

10

The answer is: 10 seats.

Directly across means exactly half-way round the table. From seat 3 to seat 8 is 8 - 3 = 5 seats. So 5 seats is half the table, and the full table has 5 x 2 = 10 seats.

Double the half-turnHalf-turn = 5 seatsWhole table = 5 x 2 = 10 seats
Diagram of the solution

Key Points

  • Opposite means half-way round
  • The number difference is the half-turn
  • Double it for the whole table

Why people get fooled

The numbers 3 and 8 pull people toward answers like 8 or 11.

Similar tricks

  • The half-turn type
  • The number-difference type

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