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# Inshi no Heya

Inshi no Heya, meaning 'factoring rooms', is a Nikoli puzzle in which the aim of the game is to add the numbers 1 to 5 on a 5x5 grid in such a manner that each row and each column has each number appear once. However, you also have to make sure the product of numbers in each room adds up to the little number hint in that room.
While the game is traditionally played on a 5x5 grid, you could play it on any sized grid, but the bigger the grid the bigger the challenge usually becomes. Part of the challenge does come from the rooms with hints on the map however.

The rules simple:
- Each row and each column can only have 1 of each number.
- The product of each number on a cell within a single room must equal the number given by that room. So if a room states '5' as its product and has 2 cells, one cell will contain a 1, and one cell will contain a 5.

## Standard version

Solving an Inshi no Heya puzzle is pretty straight forward. The first place you want to look is in any room number which can only have one possible solution in terms of its factors, meaning if a room has 6 as its number and has 3 cells, the only possible numbers in that room are 1, 2 and 3, because 1 x 2 x 3 = 6.
Before you say "What about '1 x 1 x 6'?", remember that each row and each column can only have one of each number. This would break that rule.

Once you've solved some of the easier ones it usually becomes a matter of deduction to figure out the rest. This game is a lot like Sudoku, another Nikoli puzzle, which you might be familiar with already.

## Converting it to an RPG setting.

Inshi no Heya is a little trickier to convert to an RPG setting. It could definitely work as some strange security system in which the answer is a strange, math based pass code, or perhaps as a metaphor-like way of distributing goods equally among different houses or factions based on their needs (the number in each room would be their need).

In my example I decided to go for a more magic oriented adaptation. My character finds herself locked in a room by a puzzle/math enthusiastic mage. She's given 25 small marbles, 5 of each color (red, green, yellow, blue and cyan), and is told to place one marble on each tile of the room according to the rules of Inshi no Heya.
She knows the value of each color (green equals 1, red equals 2, etc.), she can see the outlines of each 'room' and the value these require.

All she has to do is place the right marble on the right tile. There is one 'but' however, as soon as she places a marble on any tile it'll expand into a large, magic filled orb. This magic will allow her to exit the room, assuming she solves the puzzle correctly. But if she ends up placing an orb in such a way that it breaks the rules, the orb will explode and deal damage to her.

Inshi no Heya definitely requires a little more creativity in order to adapt it to an RPG setting, but there's still plenty of ways of doing it. I've mentioned a few already, but you could also convert the numbers to different kinds of power. Put too much of it in any room, column or row and you destroy everything. Or perhaps the numbers are actually people or creatures, put the wrong types together or too many of a kind and you'll cause chaos.

On a final note, if you're going to create this puzzle yourself make sure you create the grid of numbers first. It's far easier to add the rooms and math afterward.
Also, rooms can only be 1 cell wide or long. So you can have a room of 5x1 and a room of 1x4, but not one of 2x2 for example.