# Coffee Break: Square Number Maze

#### Otis

##### Senior Member
A maze involving 30 consecutive numbers covers the entire array below. The path goes horizontally and vertically only. A few random numbers have been provided. Find the beginning and ending numbers, by filling in the grid.

Rich (BB code):
[] [] [] 70 [] []
[] 53 [] [] 58 []
[] 42 55 [] [] []
[] [] [] [] [] []
[] [] [] 62 [] []

#### ksdhart2

##### Senior Member
Another nice one. Not too bad, so long as you take it one number at a time - first figure out where the 54 has to go, then the 56, etc. Full solution below:

Rich (BB code):
51 52 71 70 69 68
50 53 54 57 58 67
49 42 55 56 59 66
48 43 44 61 60 65
47 46 45 62 63 64

#### topsquark

##### Full Member
A maze involving 30 consecutive numbers covers the entire array below. The path goes horizontally and vertically only. A few random numbers have been provided. Find the beginning and ending numbers, by filling in the grid.

Rich (BB code):
[] [] [] 70 [] []
[] 53 [] [] 58 []
[] 42 55 [] [] []
[] [] [] [] [] []
[] [] [] 62 [] []
I'm not going anywhere near this one. It looks too adictive.

@Otis: Is that a typo?

-Dan

#### Otis

##### Senior Member
â€¦ take it one number at a time â€¦
Ya got it!

I had started with the smallest given number first and worked backwards -- so, basically the same process. (Didn't take long to find the smallest number, heh.)

$$\;$$

#### ksdhart2

##### Senior Member
Here's another one, if someone else wants to have a go. Hopefully I did it right and ensured it has a unique solution.

Rich (BB code):
64 [] [] 59 [] []
[] 50 [] [] [] 36
[] [] [] [] [] []
[] [] 53 42 [] []
[] [] [] [] [] []


#### Dr.Peterson

##### Elite Member
Not bad. My answer:
35 -> 64
Rich (BB code):
64 63 62|59 58|35
49 50|61 60|57|36
48|51|54 55 56|37
47|52 53|42 41|38
46 45 44 43|40 39
I wonder what it would take to make one of these harder, so that for example you would have to hold off on a couple possibilities for filling one gap, to see which one interfered with another.