A friend and I are playing a cooperative game. He has two D7 dice and 5 cards in front of him. They read;
HIDDEN IS <= SHOWN HIDDEN IS >= SHOWN HIDDEN IS EXACTLY ONE AWAY FROM SHOWN HIDDEN AND SHOWN SUM TO AN ODD NUMBER HIDDEN IS ONE OF 1/4/7
The game works as thus; my friend rolls two dice and looks at both of them. He then places one of those two dice on one card (thereby revealing it to me). That die is the SHOWN die, and the one he did not place is the HIDDEN die. He may only play a die on a card if that placement would make a true statement.
The problem is that we're both perfect logicians, so most games go pretty easily. That is, until one day he decided to mess with me. Without showing either of the dice he rolled, he gave me a few facts about his dice;
I could put either of these dice on any of at least two cards and I wouldn't be breaking any of the rules.
The lesser of them could go on more cards than the greater.
And if I removed this card, then the two previous facts would still be true.
As he said the third fact, he pointed to a card.
"I still don't know what dice you have," I said.
What card did he point to?
Thanks for playing! Inspiration for this puzzle came from the boardgame Shipwreck Arcana, it's one of my favourite games I've ever played :)