Can you outsmart Fate and break her ancient curse?

==========【原文】==========

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. 

==========【译文】==========

传说，几百年前你的远祖从命运手上偷走了一叠神奇的塔罗牌。如今，你的家族被世人认为是世界上最伟大的占卜师。虽然这副牌让你的财富与日俱增，随之而来的是可怕的代价。每隔23年，一扇门会出现在你的房子里。你的一位家庭成员必须进入，并在决斗中面对命运，而且只有你的对手知道神秘的规则。而每一次，一代又一代，结果都是一样的：命运夺去了他们的灵魂。23年前，你父亲接受了挑战然后输了。

今天，轮到你了。

你在决斗室中踱步，突然发现了一个可能改变一切的东西：你父亲在房间里藏了一台相机。

录音带显示，他把大阿卡那牌的22张牌摆了出来。命运又出了一张灵魂牌，说道：“你可以拿走桌上至少有一个因数的牌。然后我会收走它的因数对应的牌。以塔牌为例。它是16，因数为1、2、4和8。这些牌现在都归我了，所以我们是16比15。如果你在比赛结束时的总和比我高，那就你赢。再玩一次，如果我知道你没招了，我就会把剩下的牌都拿走。”

随着游戏的继续，命运说，如果你的父亲要赢了，手上还拿着10号牌，那就会给他巨大的财富。拿着6号牌（恋人），就会获得真爱。拿着2号牌（女祭司）就可以永远结束家族诅咒。但这些都不重要，因为最后，他的总和会输。

视频播完了，命运来了。你感觉好像在梦中，听到她给了你塔牌，开始了游戏。

你怎么才能打败命运，你还能为自己赢得什么财富呢？

暂停一下，自己想一想。答案在3秒后揭晓，

答案在2秒后揭晓，

答案在1秒后揭晓。

如果你想胜过命运，你需要从长远来看。接受16会给命运1、2、4和8。她绝对能拿到23、19、17和13，因为只要1不在桌子上，你就不可能拿走素数牌。小的素数，如11、7、5和3也会交给命运，但是你可以取它们的倍数，比如22和21。

剩下的就是这些牌。向下取整，你最后最多可以得到其中的一半，因为你每拿走一张牌，命运至少可以拿走一张牌。所以你的最佳选择就是拿七张最大的牌。将这些与16加在一起，你的总和将是138。命运的分数是多少？也是138。如果打平，算是命运赢，所以很明显，在解释完整规则之前把16交给你的祖先，命运一直在操纵游戏，以保证她的胜利。但多亏了你父亲，你现在更明白了。

说到你的家人，如果你想拿2去打破诅咒，你必须在你的第一回合就这么做，因为它是一个素数。如果你这样做了，命运就会拿到1，同样，命运绝对能拿到大的素数。

理论上，在剩下的17张牌中，你最多能拿到8张。拿下最大的八张牌会让你以140比136的微弱优势获胜。但这可能吗？

你每拿一张牌，都得让命运拿走尽可能少的牌。你可以从22和14开始。然后7会被拿走，你可以拿21，然后15。你还是需要这些牌的，你拿的下一张牌会让命运拿走两张牌。不过没关系。以16为例，命运得到4和8，但你可以拿走12、18和20。

同样的道理，你可以在第一回拿23，赢走10或6。但你不可能赢走超过一个奖励。那么你会选财富、爱，还是打破诅咒？命运在等待，但选择取决于你。