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# The Liar, the Truthteller, and...cake!

## Question

You have received a royal invite to the Queen of Hearts' tea party. She will be serving three types of scrumptious cake: vanity vanilla, crown chocolate, and royal red velvet. However, your confidential informant, the white rabbit, whispers to you that the Queen is very finicky and the only thing she adores more than cake is parting her subjects from their heads.

First off, you most definitely may NOT refuse the invitation. If you do, there is no place in all of Wonderland where you may hide from her wrath (hell haft no fury and whatnot ).

Secondly, her preference order for the cake flavors changes daily, and if do not partake of her cake in her preferred order...well, how would you prefer to be separated from your head?

At the entrance you'll be greeted by the Maitre D's, Tweedle Dum and Tweedle Dee, one who always lies and one who always tells the truth, albeit for the life of you you won't be able to tell the difference. WR lets you in a little secret: if you slip ONE of them a 'lil sumth'n' he'll answer ONE question of the yes-no variety.

Also, WR thinks that (for a fee, of course) he can get that irascible spy Cheshire to cop up which cake is neither the Queen's favorite or least favorite for the day. However, as WR has time management issues, he won't arrive with this tidbit of info until AFTER you've passed the D's.

Seeing how attached you are to your lovely visage, what question would you ask?

## Recommended Posts

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Assuming that the info from the Cheshire cat is true, we will know which cake is in the middle. So I would ask Dee "How would Dum answer the question 'Is the name of the queen's favorite cake alphabetically before the queen's least favorite cake?'" The opposite would be true. Then depending on the info I get from the cat I can decide on the correct order to eat the cake.

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Assuming that the info from the Cheshire cat is true, we will know which cake is in the middle. So I would ask Dee "How would Dum answer the question 'Is the name of the queen's favorite cake alphabetically before the queen's least favorite cake?'" The opposite would be true. Then depending on the info I get from the cat I can decide on the correct order to eat the cake.

ask one of the twins what the other will answer and you know you will always get a lie.

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I would ask them which cake she likes most of all this day. The one that tells the truth will give the same answer as the one who lies the most thereofre giving the same answer.

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Assuming that the info from the Cheshire cat is true, we will know which cake is in the middle. So I would ask Dee "How would Dum answer the question 'Is the name of the queen's favorite cake alphabetically before the queen's least favorite cake?'" The opposite would be true. Then depending on the info I get from the cat I can decide on the correct order to eat the cake.

Hmm...that's pretty clever, but after falling down a rabbit hole into a bizarre land where the Queen makes edicts on whim, maybe it's best not to assume that things like the order of the alphabet are the same as in the land you're from...or even that the custom is to order alphabetically by the first letter .

Edited by Yoruichi-san
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I would ask either one of Dee or Dum, "If I were to ask you whether the Queen likes Chocolate better than Vanilla, what would you say?" By asking the question this way, I am guaranteed a truthful response, which gives me the relative ordering of chocolate and vanilla in the Queen's preferences. For sake of argument, say she prefers Chocolate over Vanilla. Then, once I know the Queen's "middle" preference: if it is Vanilla, the order is Chocolate, Vanilla, Red Velvet. If her middle preference is Chocolate, then the order is Red Velvet, Chocolate, Vanilla. If her middle preference is Red Velvet, then the order is Chocolate, Red Velvet, Vanilla.

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