Legend has it, hundreds of years ago
a distant ancestor of yours stole a magical tarot deck
from Fate herself. Today, your family is known the world over
as the world’s greatest fortune tellers. While the deck has increased
your fortunes many times over, it came with a terrible cost. Once every 23 years,
a door appears in your house. One member of your family must enter, and face Fate in a duel with arcane rules
only known to your opponent. And every time,
generation after generation, the outcome is the same: Fate claims their soul. 23 years ago, your father accepted
the challenge and lost. Today, it’s your turn. You’re pacing the dueling room
when you stumble across something that just might change everything: your father hid a camera in the room. The tape shows him lay
out the 22 cards of the major Arcana. Fate then places an additional card,
the Soul, and speaks: “You may take any card that has
at least one factor on the table. I’ll then receive every factor. Take the Tower, for example. It is 16, with factors 1, 2, 4, and 8. Those now belong to me,
making our score 16 to 15. If your total at the end of the game
is higher than mine, you’ll win. Play again and know that if you
run out of moves, I’ll take all the cards that remain.” As the game continues, Fate remarks that if your father
were to win and hold the 10, that would grant him great fortune. 6, true love. And the 2 would end
the family curse forever. But none of that matters because
in the end his total comes up short. As the video turns to static,
Fate arrives. Feeling as if you’re in a dream, you hear her offer you the Tower
to begin the game. How can you defeat Fate, and what other good fortune
can you win for yourself? Pause here to figure it out for yourself.
Answer in 3 Answer in 2 Answer in 1 If you want to outplay Fate,
you’ll need to take the long view. Accepting the 16 gives Fate
the 1, 2, 4, and 8. She effectively has the 23, 19,
17, and 13 too, since you can’t take prime numbers
once 1 is off the board. Smaller primes like 11, 7, 5, and 3
will also go to Fate, but you’ll be able to take
their multiples, like 22 and 21. That means these are the remaining
cards in play. You can eventually claim at most
half of them, rounded down, since Fate gets at least one
for each card you take. So the best you can possibly do is
take the seven largest cards. Add those together with the 16
and your total would be 138. And Fate’s total? Also, 138. Ties go to Fate, so it’s clear that
by offering your ancestors the 16 before explaining the full rules, Fate has been manipulating the game
to guarantee her victory. But thanks to your father,
you now know better. Speaking of your family, if you want
to take the 2 and break the curse, you’ll have to do it on your first turn,
since it’s prime. If you do, Fate will get 1, and once again,
Fate is guaranteed the high primes. In theory, you can get at most
8 of the remaining 17 cards. Taking the eight largest would give
you a nail-bitingly narrow victory of 140 to 136. But is it possible? You need Fate to get as few cards
as possible for each one you take. You can start with the 22 and 14. With the 7 gone,
you can take the 21, then the 15. You still need these, and the next one
you take will give Fate two cards. That’s okay though. Try the 16, for example,
and Fate gets the 4 and the 8, but you’ll still get the 12, the 18,
and the 20. Following similar reasoning, you could take the 23 on your first turn
and win the 10 or the 6. But claiming more than one
reward is impossible. So do you take wealth, love,
or break the curse? Fate is waiting,
but the choice is up to you.
