## Hand dice problem

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### Hand dice problem

Harry and Julie want to create an even dice of d6. They can only use their hands and fingers. How can they achieve this by just showing their hands once?
How big eyed dice can they create?
kalakuja

Posts: 40
Joined: Sun Feb 06, 2011 10:15 am UTC

### Re: Hand dice problem

I assume you mean they want to use their hands instead of dice?
So basically, each person has to choose a number of fingers to display, but the outcome still has to appear random to each person regardless of their choice?

In that case:

Spoiler:
Just get each person to choose (randomly!) a number of fingers to display from 0 to 5. (This is nice because it works on one hand.) Then, add the totals together modulo 6. No matter what you choose, the total has an equal chance of being any of the 6 numbers (one number for each option the other player might pick).

And in the general case:
Spoiler:
Because they have 10 fingers, there are 11 different numbers of fingers that they can display. So the biggest dice they could mimic using this method would be a 'd11'. (Add the numbers together modulo 11.)
However, because they can encode larger numbers on their fingers - each finger is really a 'bit' and can be on or off - they can really display 2^10 = 1024 numbers. So they could use their hands as a d1024: Each person displays a number between 0 and 1023, and then they add both numbers together modulo 1024.

This is an awesome puzzle btw, thanks for posting it!
I will definitely use this if I don't have any dice in future!!!

dudiobugtron

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Location: The Outlier

### Re: Hand dice problem

dudiobugtron wrote:In that case:

Spoiler:
Wouldn't the first random pick (0-5) already be a d6, without the other person being involved at all?

t1mm01994

Posts: 297
Joined: Mon Feb 15, 2010 7:16 pm UTC
Location: San Francisco.. Wait up, I'll tell you some tales!

### Re: Hand dice problem

That was fast gj
t1mm01994 wrote:
dudiobugtron wrote:In that case:

Spoiler:
Wouldn't the first random pick (0-5) already be a d6, without the other person being involved at all?

Spoiler:
By random he supposedly means that it doesn't matter which finger he picks as you can't really make any tactic to get the number you want.
kalakuja

Posts: 40
Joined: Sun Feb 06, 2011 10:15 am UTC

### Re: Hand dice problem

Spoiler:
Ooops! I agree, 'random' wasn't the best word for that! Thanks for clarifying what I meant kalakuja. I should have said : "Just get each person to choose (arbitrarily!) a number of fingers to display from 0 to 5."

Spoiler:
You could actually get much higher than a d1024, if you're able to use your hands and fingers in any way you like. You could add two extra 'bits' by using your hands as extra fingers, and having them either 'up' or 'down' as well. You could also add intermediate finger and hand positions (there are lots of different, easily distinguishable positions your hands could take, since each hand can face any of the 6 'cartesian axis' directions, in any of 4 orientations (although some might be hard to do quickly!)). And of course you could also throw in things like having your hands at different heights etc...

Even just using 'finger binary' to get the first 1024, and then putting each hand in one of the 24 different poses, you get 1024x24x24 = 589824 different numbers you could encode. I don't know why anyone would need a d589824, or how easy it would be to work out what the number actually was (since you have to change bases half way through!), but I guess it just shows how amazing hands are for encoding information. Although, sign-language users already knew that!

dudiobugtron

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