# Cool Game/Fun Math Challenge



## Joe4 (May 5, 2011)

My son got a neat game for his birthday called “Spot It”.  It is a simple game to play.  There are 55 cards, each with 8 different objects on them.  You flip over two cards, and the first person to spot a “match” between the two cards wins the hand.  
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Here is the really cool thing.  You can pick up any two cards, and there is always exactly one match between the two cards.
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I find the concept fascinating, and wonder if anyone can explain:
1.  How they ensure there is one, and any only one match between any two cards?_<o></o>_
2. Exactly how many different objects do you need to do this (knowing that there are 55 cards, each with 8 objects on them)?


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## Cindy Ellis (May 5, 2011)

Well...the stupid easy answer would be that there could be just 1 item in common across all 55 cards, with only the position of that object changing from card to card, with 385 other random objects distributed across the cards.  That would make for a pretty boring game though, if you figured out that there's an apple on every card, for instance, because then you'd just have to look for the apple.
There's got to be a better answer though, but I may not be smart enough to figure it out 

Cindy


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## pgc01 (May 6, 2011)

Hi Joe, Cindy

If you know French, there's an explanation here:

http://images.math.cnrs.fr/Dobble-et-la-geometrie-finie.html


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## Joe4 (May 6, 2011)

> Well...the stupid easy answer would be that there could be just 1 item in common across all 55 cards


No, it isn't that way (I would've been able to figure that one out!).

PGC,
The link you provided actually is the game (the pictures are exactly the same as the one he has, except we have the English version).  Sadly, I do not know French.


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## SuperFerret (May 6, 2011)

Can you not get your web browser to translate? I don't know French that well and I jsut translated the page. Interesting read


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## Joe4 (May 6, 2011)

> Can you not get your web browser to translate?


To be honest, I never knew that functionality exists.  How do you do that?

I have used programs like Yahoo's Babelfish before, but the translations don't always make too much sense!


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## JamesW (May 6, 2011)

Translated:

http://translate.google.com/translate?hl=en&sl=fr&u=http://images.math.cnrs.fr/Dobble-et-la-geometrie-finie.html&ei=peTDTeGqCMHLhAfIqfX3Aw&sa=X&oi=translate&ct=result&resnum=1&ved=0CCEQ7gEwAA&prev=/search%3Fq%3Dhttp://images.math.cnrs.fr/Dobble-et-la-geometrie-finie.html%26hl%3Den%26client%3Dfirefox-a%26hs%3DSiK%26rls%3Dorg.mozilla:en-GBfficial%26prmd%3Divns

Note - It wont be the best translation!


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## Joe4 (May 6, 2011)

James, that's not too bad of a translation, just a few odd statements, like: 


> For any two points of the plan's always exactly right.


 
You can get the concept though.

There is one question I am not sure it answers though, and that is:
"Exactly how many different objects do you need to do this?"
(unless I missed it - I haven't had a chance to really go through it with a fine tooth comb).


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## schielrn (May 6, 2011)

In Spot It there are 50 different symbols, but I'm not sure how exactly you calculate that.

EDIT: Try seeing this:

http://math.stackexchange.com/questions/36798/what-is-the-math-behind-the-game-spot-it


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## Joe4 (May 6, 2011)

> In Spot It there are 50 different symbols, but I'm not sure how exactly you calculate that.


OK, that might actually make sense. According to the explanation, the game should actually have 57 cards, not 55.

There are 8 different symbols on each card, but on any two cards, exactly one pair match.

*57-8+1=50*

I don't know that my logic is solid or complete, but it seems to follow and arrive at the correct answer!


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## JamesW (May 6, 2011)

Can we just agree that it is magic and no one will ever know how it works? A bit like my missus... :P


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## Joe4 (May 6, 2011)

> Can we just agree that it is magic and no one will ever know how it works? A bit like my missus...


Yeah, I am one of those guys who always wants to know "how they do it".  I would really love to know how David Copperfield pulled off some of those illusions with huge landmarks (like the Great Wall of China).  Hopefully, it is not just some TV camera trick.  That would be very disappointing...


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## steve case (May 7, 2011)

Cindy Ellis said:


> Well...the stupid easy answer would be that there could be just 1 item in common across all 55 cards, with only the position of that object changing from card to card, with 385 other random objects distributed across the cards.  That would make for a pretty boring game though, if you figured out that there's an apple on every card, for instance, because then you'd just have to look for the apple.
> There's got to be a better answer though, but I may not be smart enough to figure it out
> 
> Cindy


First chuckle of my day (-:  

Your solution reminds me of The "Great Bud" card trick:

http://www.citydebate.com/florida/miamibeach/template.php?url=0104010702.htm


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