Hello everyone, I'm new to the forum. Can someone explain to me the suggested solution? It works, I solved it that way, but I'd like to understnd the principle behind it.

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Hello everyone, I'm new to the forum. Can someone explain to me the suggested solution? It works, I solved it that way, but I'd like to understnd the principle behind it.

- Abakus139
**Posts:**2**Joined:**30 October 2013

What I see is a Skyscraper in 5's in the 4 boldly coloured cells. Here's how it works:

Notice that there are exactly 2 5's in Column 2 and 2 5's in Column 5.

Now suppose that the bright green cell was not 5. Well, then the blue cell would have to be 5 (because there are only 2 5's in Column 2, right ?).

So the pink cell can't be 5. Now, because the pink cell can't be 5 and there are only 2 5's in Column 5 then the brown cell must be 5.

So we now know that if the bright green cell is not 5 the brown cell must be 5.

We can reverse this argument and start by assuming that the brown cell is not 5 and conclude that the bright green cell must be 5.

So this means that at least one of the bright green cell and the brown cell must be 5. They might both be 5 but they definitely can't both be not 5.

So what ? Well, look at the light green cell with the brown outline (that's Row 7 Column 4 or r7c4 for short). It's in the same row as the bright green cell and the same box as the brown cell.

But at least one of these 2 cells must be 5 so we can conclude that r7c4 can't be 5. Cross the 5 out of r7c4.

There are 3 other cells that suffer the same fate: r7c6, r8c1 and r8c3. Cross the 5's out of these cells also. r7c6 is the really good one because that means that r7c6 = 6. Pretty cool, Huh ?

Why is this pattern called a Skyscraper ?

Well, if you were to turn the puzzle upside down and look at the pattern of the 4 brightly coloured cells you'd get a pattern that looks something like this:

If you have a really active imagination you might see part of a city skyline - 2 skyscrapers. Remember, you really have to work with me here

Hope this helps.

Leren

Notice that there are exactly 2 5's in Column 2 and 2 5's in Column 5.

Now suppose that the bright green cell was not 5. Well, then the blue cell would have to be 5 (because there are only 2 5's in Column 2, right ?).

So the pink cell can't be 5. Now, because the pink cell can't be 5 and there are only 2 5's in Column 5 then the brown cell must be 5.

So we now know that if the bright green cell is not 5 the brown cell must be 5.

We can reverse this argument and start by assuming that the brown cell is not 5 and conclude that the bright green cell must be 5.

So this means that at least one of the bright green cell and the brown cell must be 5. They might both be 5 but they definitely can't both be not 5.

So what ? Well, look at the light green cell with the brown outline (that's Row 7 Column 4 or r7c4 for short). It's in the same row as the bright green cell and the same box as the brown cell.

But at least one of these 2 cells must be 5 so we can conclude that r7c4 can't be 5. Cross the 5 out of r7c4.

There are 3 other cells that suffer the same fate: r7c6, r8c1 and r8c3. Cross the 5's out of these cells also. r7c6 is the really good one because that means that r7c6 = 6. Pretty cool, Huh ?

Why is this pattern called a Skyscraper ?

Well, if you were to turn the puzzle upside down and look at the pattern of the 4 brightly coloured cells you'd get a pattern that looks something like this:

- Code: Select all
`X`

X |

| |

| |

X-------X

If you have a really active imagination you might see part of a city skyline - 2 skyscrapers. Remember, you really have to work with me here

Hope this helps.

Leren

- Leren
**Posts:**2929**Joined:**03 June 2012

Thx very much! One new technique (for me) down, plenty to go.

- Abakus139
**Posts:**2**Joined:**30 October 2013

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