# Which number goes in the square with the question mark?

My friend, who loves puzzles as much as me, gave me this image this afternoon.

My friend game me a hint: Skyscraper, which, as Daniel Mathias pointed out in the comments, is a type of grid puzzle.

• He gave me a hint : Skyscraper – SimaYi Jan 9 '19 at 20:04
• Ah, yes. Check out Skyscrapers on BrainBashers or search Google for 'skyscraper puzzle' – Daniel Mathias Jan 9 '19 at 20:14
• Thanks a lot^^ I'll look into this tomorrow morning^^ – SimaYi Jan 9 '19 at 20:42

Complete Solution to the skyscraper puzzle:

$$\begin{array}{|c|c|}\hline5&4&3&1&2\\\hline1&2&5&4&3\\\hline3&1&2&5&4\\\hline2&5&4&3&1\\\hline4&3&1&2&5\\\hline\end{array}$$

• How pretty. $(+1)$ :D – Mr Pie Jan 12 '19 at 8:53

The answer, as Daniel Mathias has given you, is

4

You do not need to solve the entire puzzle to get there, though. (Although it is entirely possible to solve the whole thing with the information given.) I was able to answer your question in 6 steps.

A.)

The 1 above the top left box makes that box "5".

B.)

The 4 to the right of the top row means that the rightmost cell must be a 1 or a 2; this is also true for the rightmost cell in the fourth row.

C.)

The bottom cell in the rightmost column must be 5. [This places 3 in the second cell down and 4 in the middle cell.]

D.)

With a 5 in the bottom right cell, the leftmost cell in the fifth row must be 4.

E.)

With the 4 and 5 used up in the leftmost column, this means that the fourth row, second cell (left) must be 5, and the middle cell must be 4.

F.)

Looking back at the top row, with 5 on the left, and a 1 or 2 on the right, there are six possible ways for the row to have 4 skyscrapers, looking from the right. However, the 4 has to be in either the target box, or the one to its right. Since step E used up the 4 in the center column, the 4 in the top row must belong to the target box.