These four mathematician friends play poker every Saturday night. They always have a twist for the very last hand, just for fun.

This Saturday the twist was “Factorial Clues”. The rule for the last hand was that every player must give a clue about his hand that relates to factorials. They played 5 card poker with a single deck.

Cards were dealt: Five each.

Here were the clues.

**John**: “I have no face cards. All my five cards are factorials. Their (five cards) multiplication is also a factorial number.”

**Jose**: “No face cards. Factorial of the first card a perfect square. Sum of the factorial of the first card and the factorial of the second card is also a perfect square. Sum of the factorial of the first card and the factorial of the second card and the factorial of the third card is also a perfect square. Sum of the factorial of the first card and the factorial of the second card and the factorial of the third card and the factorial of the fourth card is also a perfect square. Sum of the factorial of the first card and the factorial of the second card and the factorial of the third card and the factorial of the fourth card and the factorial of the fifth card is also a perfect square.”

**Ari**: “No face cards. Sum of the factorials of each of my five cards is a 3 digit perfect cube.”

**Neal**: “No face cards. None of my cards are prime numbers. My five cards add up to a number whose *reverse* is a factorial.”

It’s time to bid.

If they are all smart logical players, how should the bidding go? Specifically, what should Ari do?

Note: Ace is not a face card. It is 1 only. Please assume everything was legal.