# Quick Ripple Effect Puzzle: $70$ Empty Cells

Ripple Effect (taken from Nikoli)

• The areas divided by bold lines are called "rooms". Fill in all empty cells with numbers under the following rules.
• Each room contains consecutive numbers starting from 1 (to $$n$$ where $$n$$ is the area of the room).
• If a number is duplicated in a row or a column, the space between the duplicated numbers must be equal to or larger than the value of the number.
• Just to clarify: the "space between" means the number of cells between, not counting either end? So 1 2 1 is possible but 1 1 isn't? – Rand al'Thor Sep 4 '19 at 8:09
• @Randal'Thor that's correct – athin Sep 4 '19 at 8:18
• Is this your puzzle or from somewhere else? I just have the slightest inkling I’ve seen it somewhere… – boboquack Sep 4 '19 at 9:29
• @boboquack this is my own puzzle, if you had seen this before I guess a participant of a local competition KPK is sharing it. (So yeah, this is one of the puzzles the competition I authored.) – athin Sep 4 '19 at 10:15
• @athin Nice! __ – boboquack Sep 4 '19 at 11:02

## Step by step

• First fill in the two single-cell rooms with 1. Consider the left-hand one of these, and the two-cell room near it. If 1 is on the right of that two-cell room, then 1 can't be anywhere in the tetromino between. So we fill that two-cell room with 1 2. Then there's only one possible place for 2 in that tetromino between.

• In the next zigzag tetromino to the left, we can see which cells must be 3,4 and which must be 1,2. In the triomino above, 2 can't be at the top. That tells us where the 1 and 2 are in that tetromino, and then we can fill in that whole triomino and the top left domino.

• Now it's easy to fill in the rest of the three half-filled tetrominoes, and some stray 2s and 3s around the place:

• And then the rest of the left-hand side:

• And the rest goes smoothly to the end. (Let me know if I should add more details here, but I've shown now how the deductions work, and once half the grid is filled the rest becomes relatively easy.)

I like this game. I hope this solution can help.

• You got the first :-) Nice first answer! – Rand al'Thor Sep 4 '19 at 9:05
• Thanks but I didn't provide step-by-step pictures like you did – Adcsi Sep 4 '19 at 9:11
• Could you put your solution in a spoiler block, please? – boboquack Sep 4 '19 at 9:26
• I'm going to accept @Randal'Thor solution as it is more comprehensive, but +1 for fast solving! :D – athin Sep 4 '19 at 10:16
• (sorry, "the" should be "there" in my first comment - too late to correct) – Rand al'Thor Sep 4 '19 at 10:30

So I got a different answer than the accepted one, I assume that means I made a mistake somewhere. Can anyone help me spot it?

• In the third row, the gap between the second 4 and the third 4 is just two. – hexomino Sep 5 '19 at 14:58
• Ah, thank you! I guess I will have to re-do it. – mihomir Sep 5 '19 at 15:29