Can You Outsmart Fate and Break Her Ancient Curse?

For generations, your family has been haunted by a curse stemming from a stolen magical tarot deck. Every 23 years, a family member must face Fate in a duel, with the soul as the ultimate prize. Now, it's your turn. Armed with a hidden recording from your father's previous encounter, you have a chance to break the cycle. Can you outsmart Fate and rewrite your family's destiny?

The Terms of the Duel

Fate presents a game using the 22 cards of the Major Arcana, plus an additional card called the Soul. The rules are simple, yet deceptive:

• You may select any card that has at least one factor remaining on the table.
• Fate then receives all the factors of that card.
• The goal is to have a higher total score than Fate at the end of the game.
• If you run out of moves, Fate claims all remaining cards.

The Stakes

During your father's duel, Fate hinted at the potential rewards:

• The 10 card: Great fortune.
• The 6 card: True love.
• The 2 card: End the family curse forever.

Decoding Fate's Strategy

Your father's recording reveals a critical detail: Fate offers the Tower (16) at the beginning. This seemingly generous offer is a calculated move to manipulate the game in her favor. By taking the 16, you give Fate its factors: 1, 2, 4, and 8. She also effectively controls the prime numbers (23, 19, 17, and 13) since you can't take them once 1 is gone. Smaller primes like 11, 7, 5, and 3 will also inevitably fall into Fate's hands, allowing her to control the board.

The Path to Victory

To defeat Fate, you must think strategically and consider the long-term implications of each move. Here's a breakdown of the optimal strategies:

The Trap of the Tower

Accepting the 16 seems tempting, but it leads to a tie, which Fate wins. This is because you can claim at most half of the remaining cards (rounded down). The seven largest cards, combined with the 16, result in a tie of 138, ensuring Fate's victory.

Breaking the Curse

To break the curse, you must take the 2 on your first turn, as it's a prime number. This gives Fate the 1, and she's guaranteed the high primes. However, you can still achieve a narrow victory by claiming the eight largest of the remaining 17 cards. This requires careful planning:

1. Start with the 22 and 14.
2. With the 7 gone, take the 21, then the 15.
3. Take the 16, giving Fate the 4 and 8.
4. Claim the 12, 18, and 20.

This strategy results in a score of 140 to 136, narrowly defeating Fate and breaking the curse.

Other Rewards

Alternatively, you could take the 23 on your first turn to win either the 10 (wealth) or the 6 (true love). However, claiming more than one reward is impossible. The choice is yours: break the curse, gain wealth, or find true love.

The Choice is Yours

Fate awaits your decision. Will you fall into her trap, or will you use your knowledge to outsmart her and claim your desired reward? The fate of your family, and perhaps your own soul, hangs in the balance.