Case 07 · spatial logic · Easy · About 5–8 minutes
Six friends have agreed on their seats for tea, but the host has stacked the place cards in a drawer. A few messages about neighbors and opposite seats survive.
Restore the arrangement around the table. You will need a fixed viewpoint, so the rules specify exactly how to read it.
There are six equally spaced seats around a round table. View the table from directly above. Seat 1 is at the top of your page, and seats 2 through 6 follow clockwise. Opposite seats are three places apart.
The guests are Fern, Gus, Hana, Jules, Kai, and Luz. Each takes one seat, and every seat is used.
- Fern sits in seat 1.
- Hana is immediately clockwise from Gus.
- Jules sits opposite Fern.
- Kai sits opposite Hana.
- Luz is immediately clockwise from Jules.
Give the guests in clockwise order, beginning with Fern.
“Immediately clockwise” means the next seat in the numbered direction, including the wrap from seat 6 to seat 1. It does not mean a guest's personal left or right. Guests are not allowed to change seats during the puzzle.
Draw six small circles if you like. Start with the fixed seat and the opposite pair before trying to fit the adjacent pair. The artwork's chair positions and number of cups are decorative, not additional clues.
Hint 1 - reveal when you want a nudge
Fern fixes seat 1, so Jules must use seat 4. Luz then has a forced seat too.
Hint 2 - reveal when you want a nudge
After placing Fern, Jules, and Luz, only seats 2,3,6 remain. Which two form a clockwise neighboring pair?
Reveal the solution and explanation
The clockwise order is Fern, Gus, Hana, Jules, Luz, Kai.
Fern sits in seat 1. Jules sits opposite, in seat 4. Luz is immediately clockwise from Jules, so Luz takes seat 5.
The empty seats are 2, 3, and 6. Gus and Hana must occupy two consecutive clockwise seats, with Hana second. The only available such pair is 2–3. The possible wrap pair 6–1 is blocked by Fern; 3–4 is blocked by Jules; and 5–6 is blocked by Luz.
Therefore Gus sits in 2 and Hana in 3. Kai takes the remaining seat, 6, which is indeed opposite Hana's seat 3.
All six seats are now fixed. Viewing the table from below would reverse clockwise, but that is explicitly excluded by the overhead viewpoint. The answer therefore has no rotational or reflected alternative under the stated numbering.
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