# How to solve this 0hn0 position?

What should be my next step in this game of 0hn0?

I've managed to get this far, but none of the numbers are completed except the "1" in the top right, and there are so many possibilities for how each of the other numbers could be completed (e.g. the lower left "2" has one completed and the other one could be in any of the three directions; the lower right "3" could be completed just downwards, or to left and right, or left and down).

What can I deduce at this point about any of the cells in the grid?

• I like this game :) played a couple of times 9x9, and it is fun... – Oray Jan 8 '17 at 8:22
• I like this game, too! Aiming for a fast timing now that I already know most of the tricks (if not all). My best for the sizes (4x4 to 9x9) are 2s, 5s, 8s, 18s, 27s, and 58s. =D – justhalf Jan 9 '17 at 3:56
• @justhalf So few seconds? :-O – Rand al'Thor Jan 10 '17 at 15:02
• Wth I just had this exact board – Oliver Ni Jan 10 '17 at 23:09
• Rand al'thor, stuck? Impossible! – boboquack Jan 11 '17 at 5:39

I know you've already finished the game, but want to give a full answer.

Let's assign numbers from 1 to 5 to the rows and letters from A to E to the columns. We can figure out that:

1. The circle at C5 can see 5 circles, so C4 must be blue.

2. Since the circle at B4 can already see B5 and C4; A4, B3 and D4 are red.

3. Because the circle at B5 can see 5 circles, A5 and E5 must be blue.

4. The circle at A1 must also see B1, so the latter is blue.

5. The circle at C5 can't see any more circles, making C3 red.

6. Since the circle at C2 can see 3 circles, B2 and D2 must be blue.

7. D3 now already sees enough circles, so E3 must be red.

• Very nice indeed! This answer would actually work as a good tutorial for 0hn0; there are several different techniques used here. I may end up accepting this answer (with apologies to Deusovi). – Rand al'Thor Jan 8 '17 at 12:10
• Also, I changed the spoilertags so that people can go through the answer bit by bit, perhaps working out some of the steps for themselves, rather than seeing the whole thing at once. Hope you don't mind. – Rand al'Thor Jan 8 '17 at 12:12

Look at the 5 in the bottom middle. It can see horizontally only up to 4 spaces, so it must see vertically at least 1. Therefore the dot above it should be blue.

• @randal'thor I just lost The Game – TrojanByAccident Jan 9 '17 at 2:10

If D4 is blue, then we can see that the 2 on C4 and the 4 on E4 are completed, and so E1, E5 and B4 are red. But now to complete the 5's at E2 and E3, D3, C3 and C2 must be blue, meaning the 2's at both D2 and C4 can see more than two.

Assuming then that D4 is red, we know E1 and E5 are blue from the 4 at E4 and D3 from the 5 at E3. So D1 and C2 are red in order to block the 2 at D2, and C3 is red in order to block E3(5). The rest of the grid follows easily.

• Please improve your answer to make some sense. What are the capital letters? – Matsmath Jan 10 '17 at 15:15

@Nautilus has a good answer, but I'd like to point out a quick thing that numbers joined by blue in a row or column are 'linked'. For instance on the bottom row the 5,5,4 tell you a great deal. The two fives must extend the same distance upwards, and the 4 must extend one less upwards since they will all share the same horizontal count. Therefore since there is a '2' above the left-most '5', there must be a blue above the '5' to the right of it:

That completes the '2' above the left-most '5' so red dots go above and to the left and 2 to the right of it. Since that tops the left '5', the right '5' is topped also since it extends vertically the same distance. The rest is easy: