How many clicks would you need to finish this game?

[amalia]

Hey there,

I don't know exactly how to sum it up, but my boyfriend and I are playing a game and yesterday we had a debate on how many (mouse) clicks you would need to finish it.
We're no math experts, we're both sure our version is right, and if one of us is mistaken, I'd really appreciate an explanation.
The game goes like this: you start off with four elements: air, earth, fire and water. Out of this four elements you have to create other 556 elements (eg. air + air = pressure; earth + fire = lava; lava + water = obsidian etc.). So, you'll end up with a total of 560 elements. To create a new element, you can only combine two other elements (never three or more). Some of these elements are so-called 'final elements', meaning that they can not be mixed up with anything else to create something new. Anyway, I don't think this info is relevant.
After we were both stuck around 500 elements discovered, we asked ourselves how many mouse clicks you would need to try out every combination possible.
My version: 560 * 560 (560²) - ofc, I counted the final elements.
My boyfriend's version: 560⁵⁶⁰ (560 multiplied with itself for 560 times).
So - who's right? Maybe none of us, :-D

 

[Harry_the_cat]

Hey there,

I don't know exactly how to sum it up, but my boyfriend and I are playing a game and yesterday we had a debate on how many (mouse) clicks you would need to finish it.
We're no math experts, we're both sure our version is right, and if one of us is mistaken, I'd really appreciate an explanation.
The game goes like this: you start off with four elements: air, earth, fire and water. Out of this four elements you have to create other 556 elements (eg. air + air = pressure; earth + fire = lava; lava + water = obsidian etc.). So, you'll end up with a total of 560 elements. To create a new element, you can only combine two other elements (never three or more). Some of these elements are so-called 'final elements', meaning that they can not be mixed up with anything else to create something new. Anyway, I don't think this info is relevant.
After we were both stuck around 500 elements discovered, we asked ourselves how many mouse clicks you would need to try out every combination possible.
My version: 560 * 560 (560²) - ofc, I counted the final elements.
My boyfriend's version: 560⁵⁶⁰ (560 multiplied with itself for 560 times).
So - who's right? Maybe none of us, :-D

Does each "creation" take 2 mouse clicks?

 

[amalia]

Yes. It takes two mouse clicks.
The game is called Little Alchemy, if anyone wants to check it for themselves.