Liar Slitherlink. Follow regular Slitherlink clues (make a loop following the gridlines that doesn’t touch/cross itself anywhere, and givens tell the number of sides used around that cell). However, exactly one given in each row/column is wrong. The task of determining which givens are lying is given to you.
It was a tough journey, but Sky made it to Odd Island. He was pretty surprised to see a few zeroes; perhaps the zeroes betrayed Even Island inhabitants? In any case, he managed to avoid suspicions, and in case someone attacked him (he’s #492, so yeah), he simply Seed Flared them away.
He made it to the prison that he suspects to hold many of the twos, and boy, what a surprise! No less than 86 twos are present. They sure kidnapped a lot of twos! He wanted to free them all from those pesky guards, but he surely could not Seed Flare those innocent twos. So he went with a very unusual approach…of Liar Slitherlink-ing them.
Wait… Isn’t Sky’s previous puzzle a Liar Slitherlink? Is Sky our hero? Hm…
Yes, MellowMelon-inspired. Although I don’t think he made that for the purpose of maximizing the number of 2s; mine started with a grid of 2s and givens got replaced when they don’t fit.
Also, if you’ve solved the grid, you may continue the story:
Sky’s bizarre strategy worked! Somehow. The guards were disoriented by being called liars and stuffs, and they all went arguing, allowing those twos to escape. They all went back, Sky was reunited with his lost two, and he could finally make another puzzle involving twos. Maybe next time…