Logic Challenge (The three words answer has been revealed)

[Kevin]

A logic challenge . I hope this is not instead a 'patience test' I made this.
Guess what is happening (the mysterious reaction :B ). Try to make your explanation as simple as you can (guess the pattern which applies to all reactions).

Hint:

Spoiler (Click to View)

with '--->' I mean 'becomes'
with '♦x6' I mean ♦♦♦♦♦♦
with '0' I mean empty, or '♦x0'
Hint:
0 is always placed on the left-most slot and will always be filled after the reaction.
The 'before reaction' can only contain ♦♦♦, ♦x6, and ♦x9. Ooo suspicious...

Learn the pattern from the reactions:

Spoiler (Click to View)

The simplest reactions:

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0 - ♦♦♦ - ♦♦♦ - ♦♦♦ ---> ♦ - ♦♦♦ - ♦♦♦ - ♦♦

0 - ♦x6 - ♦x6 - ♦x6 ---> ♦♦ - ♦x6 - ♦x6 - ♦♦♦♦

0 - ♦x9 - ♦x9 - ♦x9 ---> ♦♦♦ - ♦x9 ♦x9 - ♦x6

Some more complex reactions (still the same pattern)

Spoiler (Click to View)

0 - ♦x6 - ♦♦♦ - ♦♦♦ ---> ♦♦ - ♦♦♦♦♦ - ♦♦♦ - ♦♦

0 - ♦x6 - ♦x6 - ♦♦♦ ---> ♦♦ - ♦x6 - ♦♦♦♦♦ - ♦♦

0 - ♦x9 - ♦x6 - ♦x6 ---> ♦♦♦ - ♦x8 - ♦x6 - ♦♦♦♦

0 - ♦x9 - ♦x9 - ♦x6 ---> ♦♦♦ - ♦x9 - ♦x8 - ♦♦♦♦

Comparation between small and bigger reactions:

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0 - ♦♦♦ - ♦♦♦ ---> ♦ - ♦♦♦ - ♦♦

0 - ♦♦♦ - ♦♦♦ - ♦♦♦ - ♦♦♦ - ♦♦♦ ---> ♦ - ♦♦♦ - ♦♦♦ - ♦♦♦ - ♦♦♦ - ♦♦

0 - ♦x6 - ♦x6 ---> ♦♦ - ♦x6 - ♦♦♦♦

0 - ♦x6 - ♦x6 - ♦x6 - ♦x6 - ♦x6 ---> ♦♦ - ♦x6 - ♦x6 - ♦x6 - ♦x6 - ♦♦♦♦

0 - ♦x9 - ♦x9 ---> ♦♦♦ - ♦x9 - ♦x6

0 - ♦x9 - ♦x9 - ♦x9 - ♦x9 - ♦x9 ---> ♦♦♦ - ♦x9 - ♦x9 - ♦x9 - ♦x9 - ♦x6

Comparation when positions are swapped.

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0 - ♦x6 - ♦♦♦ ---> ♦♦ - ♦♦♦♦♦ - ♦♦

0 - ♦♦♦ - ♦x6 ---> ♦ - ♦♦♦♦ - ♦♦♦♦

0 - ♦x9 - ♦♦♦ ---> ♦♦♦ - ♦x7 - ♦♦

0 - ♦♦♦ - ♦x9 ---> ♦ - ♦♦♦♦♦ - ♦x6

0 - ♦x9 - ♦x6 ---> ♦♦♦ - ♦x8 - ♦x4

0 - ♦x6 - ♦x9 ---> ♦♦ - ♦x7 - ♦x6

If you feel like you haven't get enough clues you can ask me for example:

What will 0 - ♦♦♦ - ♦x6 - ♦x9 be ??

Just note that the 'reactant' (before reaction) must start with '0' and only contains ♦♦♦, ♦x6, and ♦x9.

Without the '0' the reaction won't happen.
If the reactant contains other than ♦♦♦, ♦x6, and ♦x9, complications will happen... there is still an answer to that, with the same rule, but nevermind that.

I don't know whether this is easy to guess or not, but I do hope it's hard lol because the answer is interesting.


There is only one pattern that makes all the reactions above.
Come on, guess what's happening . The answer is quite simple!!

Maybe this can give you some hints.. if you can't solve it from the above.

Spoiler (Click to View)

Example of first-step thinking?
0 - ♦♦♦ ---> ♦ - ♦♦
Hmm... the '♦♦♦' gives 1 ♦ to the '0'.

0 - ♦♦♦ - ♦♦♦ ---> ♦ - ♦♦♦ - ♦♦
Hmm... now only the right-most '♦♦♦' gives it to '0'.

0 - ♦x6 ---> ♦♦ - ♦♦♦♦
Hmm... so a '♦x6' gives two ♦ instead of one.

0 - ♦♦♦ - ♦x6 ---> ♦ - ♦♦♦♦ - ♦♦♦♦
Hmm... In this case it's like the ♦x6 is giving one to the ♦x3 and one to the '0'. Looks like if ♦x6 is placed on the right, it always gives 2♦. Strange... let's see more example.

Man... no more examples.. maybe I should ask some.
What will 0 - ♦x9 - ♦♦♦ - ♦x9 and 0 - ♦x6 - ♦♦♦ - ♦x6 be??

If you think you figured out the pattern, try guessing what they will be:

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1. 0 - ♦♦♦ - ♦x9 - ♦x9 - ♦x6 - ♦x9 - ♦♦♦ - ♦x6 - ♦x9
2. 0 - ♦x9 - ♦♦♦ - ♦♦♦ - ♦x6 - ♦x6 - ♦♦♦ - ♦x9 - ♦♦♦

and the last one... complications will happen, if you have not solved the simplest explanation of the reaction, you cannot answer this:
3. 0 - ♦♦ - ♦x5 - ♦x8 - ♦♦♦♦

[symaroth1]

-scratching head-

no idea this is hard nice job
but still...

[Kevin]

:o maybe this is too hard xD . Actually the answer is very simple and very short xD (only a few simple words).
First hint is that the right-most item will lose one-third of its contains.
The ♦'s lost by a slot will be received by one of the slots in its left.
Slots with less ♦ usually receives more ♦ after the reaction.
Can you figure out some pattern from the given reactions with these clues? :P Maybe at first you will get a complicated pattern, but maybe you will be able to simplify it.

[Kevin]

Hmm either this is too hard or just not interesting... :\ .
The most obvious solution is by moving a box from the right to the left in the 'before reaction' part.
The box always wants a third of the contents in each slot.

e.g.
0 - ♦x6 - ♦x6 - ♦♦♦ ---> ???

The box starts from the right, so it meets ♦♦♦ first. The box wants a third of it (i.e. 1♦)
So the box takes one ♦ from the right-most slot
Next the box moves to the left and meets ♦x6, and it will want 2♦ (a third of ♦x6)
Since the box already has one ♦, it only take one ♦ from the ♦x6. Now the box has 2♦.
The box moves again to the left and it already have a third of ♦x6 so it doesn't take anything.
When the box reach '0', it will give all ♦ it has. Since it has 2♦, it gives them all to the zero slot.

That's how
0 - ♦x6 - ♦x6 - ♦♦♦ ---> ♦♦ - ♦x6 - ♦♦♦♦♦ - ♦♦




Now I will reveal the three-words answer:
Multiplication by Four

e.g.
0 - ♦x6 - ♦x6 - ♦♦♦ ---> ♦♦ - ♦x6 - ♦♦♦♦♦ - ♦♦

open calculator, type in 663 x 4 and the answer will be 2652.