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11 tourists are standing in an ancient temple (6x6 grid).
The temple contains 16 stone tables.
Each tourist is facing either north, south, west, or east and sees a different number of tables.
The numbers in the grid indicate where each tourist is standing and how many tables they see.
Each cell holds either a tourist, a table, or nothing (no overlaps).
A tourist can see anything in front of them at 45 degree angles. Tables and tourists do not block lines of sight.

For example, in this hypothetical temple (with 6 tables marked "T"), the tourist numbered "4" is facing north and can see 4 tables. Yellow squares are in their line of sight.

EXAMPLE

Here is the actual temple. Where are the 16 tables located?
temple

Text version:

Example:  
y y T 1 T y
T y T y y -
- 3 y y - -
- T 4 - - -
- - - T - -
- - - - - -

Puzzle:  
- - 2 - - 9
- - - 0 - -
7 5 - 3 - 10
- - - - 4 -
- 6 - 1 - -
- - 8 - - -
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2 Answers 2

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This is way I solved it; there may well be a shorter and/or more elegant solution.

If 0 faces E then 2 must face W. Thus, among the sixteen still-empty squares in

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there are fourteen with tables. Then 4 must be facing S, and 1 too. So among the eleven still-empty squares in

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there are ten with tables. But then there's no direction 5 can face. So 0 doesn't face E, and must therefore face N. So we have

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Now, 8 faces N, so there must be eight tables south of 8's line of sight, which means (because 1 can only see one of them) that we have

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If 7 is facing E there's not enough room west of 7's line of sight for nine more tables, so 7 is facing S. Thus,

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Now, 10 must be facing W, so

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We need four more tables, so 5 can't be facing N, so 5 is facing E, and

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And thus

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Let's make sure all the numbers work:

0 faces N, 1 S, 2 E, 3 E, 4 S, 5 E, 6 N, 7 S, 8 N, 9 S, and 10 W: yep, it works.

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  • $\begingroup$ This is great! I think my solution was a bit shorter so I'll write that up too $\endgroup$
    – Bryce
    Commented Oct 25, 2023 at 18:40
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The solution is

T T 2 Y Y 9
T T Y 0 Y T
7 5 Y 3 Y 10
T T Y Y 4 T
T 6 T 1 T T
T T 8 T Y T

Here is my approach:

We start off with the puzzle
- - 2 - - 9
- - - 0 - -
7 5 - 3 - 10
- - - - 4 -
- 6 - 1 - -
- - 8 - - -

7 must be S (E would not provide enough T for the grid).
- - 2 - - 9
- - - 0 - -
7 5 - 3 - 10
T T - - 4 -
T 6 T 1 - -
T T 8 T - -

This forces 1S and 0N
- - 2 Y Y 9
- - - 0 - -
7 5 - 3 - 10
T T - - 4 -
T 6 T 1 - -
T T 8 T Y -

If we consider 10W, there are 8 positions not seen by 10 and 6T not seen by 10. 2 positions have Y, so the rest must be T
- - 2 Y Y 9
- - - 0 - T
7 5 - 3 - 10
T T - - 4 T
T 6 T 1 T T
T T 8 T Y T

2E and 5E place the rest of the Y
- - 2 Y Y 9
- - Y 0 Y T
7 5 Y 3 Y 10
T T Y Y 4 T
T 6 T 1 T T
T T 8 T Y T

Then we can fill in the rest of the T
T T 2 Y Y 9
T T Y 0 Y T
7 5 Y 3 Y 10
T T Y Y 4 T
T 6 T 1 T T
T T 8 T Y T

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