Sunday Times Teaser 2867 – Clumsy Meg

by Graham Smithers

Published September 3 2017 (link)

I arranged cards labelled ONE, TWO, THREE, FOUR, FIVE, SIX, SEVEN, EIGHT, NINE and TEN equally-spaced around the perimeter of a circular table. The arrangement was such that any two adjacent cards had exactly one letter in common.

That evening Meg entered the room and accidentally knocked two adjacent cards onto the floor. In her haste to put things right, she inadvertently put the two cards back the wrong way round. Surprisingly, the one-letter property still applied.

What were the two numbers directly opposite the two that she knocked on the floor?