Logic Masters Deutschland e.V.

This puzzle was created as a birthday gift for ONeill, who very supportively tested all of my first puzzles and helped me get confidence in my setting skills. I chose to make a position sums fillomino, because these are 2 of his favorite constraints, as you'll see if you look at the puzzles he set. I also added a bit of ciphering to it, because it's fun and allowed me to use the letters for the design too. I'm publishing this with his permission and encouragement. This version is slightly easier than the one he solved. I decided to modify a couple of clues to make it smoother.

Thanks to polar for testing both versions !

If you have trouble understanding how position clues work, check out the solvable example puzzle that I made to illustrate them.

Rules :

- Fillomino : divide the grid into regions so that no two regions of the same size share an edge. Enter a number into each cell equal to the size of its region.

- Position Sums : let A and B be the digits in the first and second cells of the grid from any direction (row, column, main diagonals).

a) Unshaded clues outside the grid indicate the sum of A and B

b) Shaded clues indicate the sum of the digits in positions A and B from that direction (A and B must both have valid indexing values). Note that it is possible that A and B index the same cell. If A and B index the same cell, the sum is twice the value of the cell they index.

If a clue is circled, the cells that are part of its sum belong to the same region.

If a clue is not circled, the cells that are part of its sum belong to different regions.

Clues are ciphered. "?" is a stand in for any digit 0-9, but for a double digit number, the first digit may not be 0. Each distinct letter represents some unique digit from 0 to 9. The letters appearing in grid cells will have to be replaced by the corresponding digit.

Note : the 2 dashed rectangles with "A+B" and "Ath+Bth" are not actual clues. They just show the nature of each ring of clues.

Example : SMOL

Solve on Penpa

The puzzle :

Solve on Penpa

Enjoy ! And consider leaving a comment if you appreciate the puzzle !

You can check out my other puzzles here if you liked this one.