# Coffee Break: No touching allowed

#### Otis

##### Senior Member
Use letters A,B,C,D,E,F,G,H,I,J to complete the grid below. Place one letter in each square so that no pair of consecutive letters in the alphabet occupy squares that touch in any way (not even at a corner). Three of the letters have been inserted for you.

#### lookagain

##### Senior Member
$$\displaystyle C$$
$$\displaystyle F \ \ \ A$$
$$\displaystyle I \ \ \ \ D \ \ \ J$$
$$\displaystyle \ \ \ \ \ \ B \ \ \ H$$
$$\displaystyle G \ \ \ E$$

#### greg1313

##### New member
Yes, if only mmm4444bot had not created another username "Otis," posts/threads like the one above would be under
just the one username all along. lookagain, I see you tried to give him/her "an out" by deleting that post # 16 in that
other thread. And this username, "greg1313," would not exist in response to the creation of "Otis."

But live and learn must mmm4444bot. (With apologies to Yoda.)

Note: Please keep scrolling down to see every step.

For convenience, I let A = 1, ... , J = 10.

We have the equivalent of:

$$\displaystyle *$$
$$\displaystyle 6 \ \ \ *$$
$$\displaystyle * \ \ * \ \ *$$
$$\displaystyle \ \ \ \ \ 2 \ \ \ 8$$
$$\displaystyle * \ \ \ *$$

The only place for the 7 is the far left bottom:

$$\displaystyle *$$
$$\displaystyle 6 \ \ \ *$$
$$\displaystyle * \ \ * \ \ *$$
$$\displaystyle \ \ \ \ \ 2 \ \ \ 8$$
$$\displaystyle 7 \ \ \ *$$

The only potential places for the 1 and the 3 are above the 6 and to the right of the 6.
This forces the 9 to go directly below the 6:

$$\displaystyle *$$
$$\displaystyle 6 \ \ \ *$$
$$\displaystyle 9 \ \ * \ \ *$$
$$\displaystyle \ \ \ \ \ 2 \ \ \ 8$$
$$\displaystyle 7 \ \ \ *$$

Numbers 1 and 3 are committed between two squares. We still need to place 4, 5, and 10. Look at the
square immediately to the right of the square that has 9 in it. It cannot be 10 or 5, because that would
violate the squares having 9 and 6 in them. So, it must be 4:

$$\displaystyle *$$
$$\displaystyle 6 \ \ \ *$$
$$\displaystyle 9 \ \ \ 4 \ \ \ *$$
$$\displaystyle \ \ \ \ \ 2 \ \ \ 8$$
$$\displaystyle 7 \ \ \ *$$

The rest of the numbers fall in place. The number above 4 must be 1 and the number above 6 must
be 3. The 5 must be directly below 2, and finally, 10 is to the right of 4:

$$\displaystyle 3$$
$$\displaystyle 6 \ \ \ 1$$
$$\displaystyle 9 \ \ \ 4 \ \ \ 10$$
$$\displaystyle \ \ \ \ \ 2 \ \ \ \ 8$$
$$\displaystyle 7 \ \ \ 5$$

Then, convert the numbers back to the letters of the alphabet.