Puzzle No. 478 : Christmas Loop

Just about got a crazy idea in time to execute it on Christmas day. Thanks to Chaotic Iak and Tiit Vunk for testing this one. The puzzle itself is pretty difficult. The rules are complex. So, Merry Christmas everyone! *evil laugh*

Oh and thanks to Tawan for hosting the wonderful contest Colour Restore, which I won, because I’m the KING of Rock-Paper-Scissors B-) Actually, that’s where the entire inspiration for this idea started, the colours, which is mainly why I wanted the colours to be able to help in the solve in some way. So thanks for that too.

Rules –

Part 1 – Cipher Fillomino – Using Fillomino rules, divide the grid into regions. The numbers are all replaced by colours. Same numbers are represented by the same colour, and different numbers by a different colour.

Part 2 – Regional Railroads – Draw a loop that passes through every cell of the grid and doesn’t overlap itself. It can cross only on cells with a + sign and has to cross on every cell with a + sign. Each region in the grid must have at least one continuous instance of the loop passing through all it’s cells.

Part 3 (Not necessary for the puzzle to be unique. You can skip ahead to the puzzle with the rules above without this helper) Colour Combinations – The 3 common ways that colours mix to form other colours ((Red, Blue, Purple)(Blue, Yellow, Green)(Red, Yellow, Orange)) will form 3 groups where the colour values can make the arithmetic equation A+B=C valid somehow. (e.g. Red +Purple = Blue)

Rated – Hard of course.

If you want an easier version than even the part 3 helper, here’s an image with the equations between colours directly given.

P478