Suguru (additionally is aware of as Number Blocks or Tectonic), is a well-liked sort of grid-deduction puzzle:
In an oblong grid of squares, the squares are grouped into blocks. As with a sudoku, some squares have already got a quantity. The aim is to fill the remaining squares in order that:
- A block of n squares incorporates all numbers 1 to n
- Adjacent squares (horizontally, vertically or diagonally) cannot include the identical quantity
There’s loads of Suguru/Tectonic puzzles on paper and on-line (instance)
So far the introduction…
I’ve all the time puzzled if there exists Suguru puzzles with none preliminary numbers, that but have precisely one answer.
It’s comparatively simple to indicate that such an empty Suguru puzzle would want blocks of all sizes (eg. if the most important block has 5 squares, you then additionally want blocks consisting of 1,2,3 and 4 squares).
After lots of guide makes an attempt (which led to puzzles with both no answer or a number of options), I finally wrote a pc program to resolve suguru and exhaustively seek for empty ones. It appears that there aren’t that many…
Here is an instance of an empty suguru puzzle so that you can heat up:
+---+---+---+---+---+
| | |
+---+---+---+---+---+
| | |
+ +---+---+ +---+
| | | |
+---+---+---+---+---+
Solution
From high to backside: 12321, 45143, 12321. Notice how every block has all totally different numbers, counting up from 1, and the way neighbouring grids by no means have the identical quantity.
And here is one that’s much more difficult:
+---+---+---+---+---+
| | | |
+ +---+ +---+ +
| | | | |
+ +---+ + +---+
| | | | |
+ + + +---+ +
| | | | | |
+---+ +---+ + +
| | | | |
+ +---+---+ +---+
| | |
+---+---+ + +---+
| | | | |
+---+---+---+---+---+
Can you resolve the bigger puzzle?
Bonus query: Do empty Suguru puzzles exist which are smaller than 3 by 5 and which have precisely one answer? (aside from the trivial 1 by 1, after all).
