In one of Professor Layton's games there is a puzzle that has picked my interest. I mean, I know the answer using logic, but I am not able to produce an equation, so I hope someone could help me.
"There are 52 cards in the deck below -26 black and 26 red- and no jokers.
After shuffling the deck and randomly cutting it in two, you count 23 cards in the stack on the left.
So, what's the difference between the number of red cards in the left stack and the number of black cards in the right stack?"
Thanks
Here is an approach which I believe is correct, if I understand your problem:
$$ R_{left}+B_{left}=23 \\ R_{right}=26-R_{left} \\ R_{right}+B_{right}=29 $$
Now using the above: $$ B_{right}=29-R_{right} \\ B_{right}=29-(26-R_{left}) \\ B_{right}=29-26+R_{left} \\ -3=R_{left}-B_{right} \\ $$
I hope this helps.