# Last puzzle of 2019

**URL:** <https://discourse.julialang.org/t/last-puzzle-of-2019/32820>\
**Category:** Offtopic\
**Created:** [December 31, 2019, 8:26am UTC](https://discourse.julialang.org/t/last-puzzle-of-2019/32820 "2019-12-31T08:26:27Z")\
**Posts on this page:** 6\
**Page:** 1

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**Author:** ![StevenSiew](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/stevensiew/32/218393_2.png) [@StevenSiew](https://discourse.julialang.org/u/StevenSiew)\
**Post date:** [December 31, 2019, 8:26am UTC](https://discourse.julialang.org/t/last-puzzle-of-2019/32820/1 "2019-12-31T08:26:27Z")

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“I am a time traveller!” said the time traveller. “Bullshit!” said I. “I will prove it to you. Get a fair dice. Color the side 1,2 and 3 as red. Color the sides 4 and 5 as green. And finally colour the side 6 as blue.” I did as the traveller asked.

“Now I will write down the color which you will roll” said the traveller and wrote down something on a piece of card which was placed face down so I could not see what was written.

“Roll the die!” the time traveller demanded. I did. “now watch this!” the traveller said and turn over the card.

The card showed a word correctly described the color of the side of the dice which I rolled.

Question: Assuming the time traveller is a Fraud, what is the probability of writing down the correct result on the card before I rolled the dice?

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**Author:** ![jling](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jling/32/212909_2.png) [@jling](https://discourse.julialang.org/u/jling)\
**Post date:** [December 31, 2019, 8:37am UTC](https://discourse.julialang.org/t/last-puzzle-of-2019/32820/2 "2019-12-31T08:37:43Z")

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> [@StevenSiew](#):
>
> what is the probability of writing down

depends on what’s their strategy (i.e distribution of words written down)? Clearly the most probable color would be red and that just means `1/2`, in any case, it would be the `P_red * 1/2 + P_green * 1/3 + P_blue * 1/6` each `P` depends on how this fraud is designed? (`P`s adds to `1` of course, so clearly it means `P_red == 1`?)

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**Author:** ![Tamas\_Papp](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tamas_papp/32/25949_2.png) [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)\
**Post date:** [December 31, 2019, 8:55am UTC](https://discourse.julialang.org/t/last-puzzle-of-2019/32820/3 "2019-12-31T08:55:44Z")

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Conceptually, I would look for the mixed strategy Nash equilibrium of the zero-sum game. It’s a nice intro game theory exercise.

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**Author:** ![jling](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jling/32/212909_2.png) [@jling](https://discourse.julialang.org/u/jling)\
**Post date:** [December 31, 2019, 9:02am UTC](https://discourse.julialang.org/t/last-puzzle-of-2019/32820/4 "2019-12-31T09:02:16Z")

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I don’t think there’s game theory here, roller can’t control the die

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**Author:** ![Tamas\_Papp](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tamas_papp/32/25949_2.png) [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)\
**Post date:** [December 31, 2019, 9:05am UTC](https://discourse.julialang.org/t/last-puzzle-of-2019/32820/5 "2019-12-31T09:05:49Z")

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Good point, I somehow thought that the roller writes something down too (for no good reason).

In that case, I think the best strategy is to write down the most probable color, and get it right 1/2 of the time.

But with puzzles like this, there is always some underspecified ingredient, which I usually miss.

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**Author:** ![longemen3000](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/longemen3000/32/7298_2.png) [@longemen3000](https://discourse.julialang.org/u/longemen3000)\
**Post date:** [December 31, 2019, 1:58pm UTC](https://discourse.julialang.org/t/last-puzzle-of-2019/32820/6 "2019-12-31T13:58:14Z")

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> [@StevenSiew](#):
>
> The card showed a word correctly described the color

The time traveler didn’t write a color, but a description. If there is an alternate, ambiguous description, used, maybe the time traveler added the final piece of information after showing the card, to desambiguate the result to whatever color is rolled