Solution
Six at a Round Table
Show the problem again
Six people (Ann, Bo, Cy, Di, Ed and Flo) sit at a round table with six equally spaced seats. "Beside" means in an adjacent seat, and "opposite" means three seats away. You are told: 1. Ann sits beside Bo. 2. Cy does not sit beside Ann. 3. Cy does not sit opposite Di. 4. Di sits beside Ed. 5. Bo does not sit beside Flo. 6. Ed does not sit opposite Bo. 7. Cy does not sit beside Ed. 8. Di does not sit beside Flo. The clues do not distinguish a seating from its mirror image, but they do determine who sits opposite Ann. Who is it?
Worked solution
Fix Ann in seat 0, and by mirror symmetry put Bo in seat 1. Cy is not beside Ann, so Cy is in seat 2, 3 or 4; Flo is not beside Bo, so Flo is in seat 3, 4 or 5; Ed is not opposite Bo, so Ed is not in seat 4. If Flo is in seat 4, Di (who may not sit beside Flo) must take seat 2, so Ed sits beside Di in seat 3, leaving Cy in seat 5, beside Ann: forbidden. If Flo is in seat 3, Di is not in seat 2 or 4, so Di is in seat 5, and Ed would be in seat 4 (beside Di and not Ann's seat), but Ed may not take seat 4. So Flo is in seat 5. Di cannot be in seat 4 (beside Flo), so Di is in seat 2 or 3. If Di is in seat 2, Ed must be in seat 3 and Cy in seat 4 beside Ed: forbidden. So Di is in seat 3, Ed in seat 2 (beside Di, not seat 4), and Cy in seat 4. Check: Cy is beside Di and Flo, not Ed or Ann, and is not opposite Di. The arrangement is Ann, Bo, Ed, Di, Cy, Flo around the table. Di sits opposite Ann (the mirror image gives the same answer).
Source: Original puzzle written for AxiomIQ in the style of classic seating-arrangement deduction puzzles.