2 3 1 2 1 3

then the two 1's enclose 1 other digit, the two 2's enclose 2 other digits, and the two 3's enclose 3 other digits.

Can you find a similar arrangement using the seven pairs 1,1,...7,7?

DIM taken(14)
OPEN "231213.txt" FOR OUTPUT AS #2
FOR a1 = 1 TO 12
b1 = a1 + 2
taken(a1) = 1: taken(b1) = 1

FOR a2 = 1 TO 11
b2 = a2 + 3
IF taken(a2) = 0 AND taken(b2) = 0 THEN
taken(a2) = 2: taken(b2) = 2

FOR a3 = 1 TO 10
b3 = a3 + 4
IF taken(a3) = 0 AND taken(b3) = 0 THEN
taken(a3) = 3: taken(b3) = 3

FOR a4 = 1 TO 9
b4 = a4 + 5
IF taken(a4) = 0 AND taken(b4) = 0 THEN
taken(a4) = 4: taken(b4) = 4

FOR a5 = 1 TO 8
b5 = a5 + 6
IF taken(a5) = 0 AND taken(b5) = 0 THEN
taken(a5) = 5: taken(b5) = 5

FOR a6 = 1 TO 7
b6 = a6 + 7
IF taken(a6) = 0 AND taken(b6) = 0 THEN
taken(a6) = 6: taken(b6) = 6

FOR a7 = 1 TO 6
b7 = a7 + 8
IF taken(a7) = 0 AND taken(b7) = 0 THEN
taken(a7) = 7: taken(b7) = 7
FOR i = 1 TO 14
 PRINT (STR$(taken(i)));
 PRINT #2, (STR$(taken(i)));
NEXT
PRINT
PRINT #2,
ct = ct + 1
taken(a7) = 0: taken(b7) = 0
END IF
NEXT

taken(a6) = 0: taken(b6) = 0
END IF
NEXT

taken(a5) = 0: taken(b5) = 0
END IF
NEXT

taken(a4) = 0: taken(b4) = 0
END IF
NEXT

taken(a3) = 0: taken(b3) = 0
END IF
NEXT

taken(a2) = 0: taken(b2) = 0
END IF
NEXT

taken(a1) = 0: taken(b1) = 0
NEXT

PRINT ct

finds the following 30 solutions:

 1 7 1 2 5 6 2 3 4 7 5 3 6 4
 1 7 1 2 6 4 2 5 3 7 4 6 3 5
 1 6 1 7 2 4 5 2 6 3 4 7 5 3
 1 5 1 6 7 2 4 5 2 3 6 4 7 3
 1 4 1 5 6 7 4 2 3 5 2 6 3 7
 1 4 1 6 7 3 4 5 2 3 6 2 7 5
 1 6 1 3 5 7 4 3 6 2 5 4 2 7
 1 5 1 7 3 4 6 5 3 2 4 7 2 6
 1 5 1 6 3 7 4 5 3 2 6 4 2 7
 1 5 1 4 6 7 3 5 4 2 3 6 2 7
 5 1 7 1 6 2 5 4 2 3 7 6 4 3
 4 1 7 1 6 4 2 5 3 2 7 6 3 5
 4 1 6 1 7 4 3 5 2 6 3 2 7 5
 7 1 3 1 6 4 3 5 7 2 4 6 2 5
 7 1 4 1 6 3 5 4 7 3 2 6 5 2
 6 1 5 1 7 3 4 6 5 3 2 4 7 2
 4 6 1 7 1 4 5 2 6 3 2 7 5 3
 7 3 1 6 1 3 4 5 7 2 6 4 2 5
 4 6 1 7 1 4 3 5 6 2 3 7 2 5
 5 6 1 7 1 3 5 4 6 3 2 7 4 2
 7 4 1 5 1 6 4 3 7 5 2 3 6 2
 5 7 1 4 1 6 5 3 4 7 2 3 6 2
 3 6 7 1 3 1 4 5 6 2 7 4 2 5
 5 7 4 1 6 1 5 4 3 7 2 6 3 2
 2 6 7 2 1 5 1 4 6 3 7 5 4 3
 4 5 6 7 1 4 1 5 3 6 2 7 3 2
 2 3 7 2 6 3 5 1 4 1 7 6 5 4
 3 4 5 7 3 6 4 1 5 1 2 7 6 2
 2 3 6 2 7 3 4 5 1 6 1 4 7 5
 5 2 4 7 2 6 5 4 1 3 1 7 6 3
 2 6 3 2 7 4 3 5 6 1 4 1 7 5
 2 6 3 2 5 7 3 4 6 1 5 1 4 7
 2 4 7 2 3 6 4 5 3 1 7 1 6 5
 5 2 7 3 2 6 5 3 4 1 7 1 6 4
 5 2 4 6 2 7 5 4 3 1 6 1 3 7
 3 5 7 2 3 6 2 5 4 1 7 1 6 4
 2 7 4 2 3 5 6 4 3 7 1 5 1 6
 2 5 6 2 3 7 4 5 3 6 1 4 1 7
 5 2 6 4 2 7 5 3 4 6 1 3 1 7
 5 7 2 3 6 2 5 3 4 7 1 6 1 4
 5 3 6 7 2 3 5 2 4 6 1 7 1 4
 3 4 6 7 3 2 4 5 2 6 1 7 1 5
 7 2 6 3 2 4 5 3 7 6 4 1 5 1
 7 2 4 6 2 3 5 4 7 3 6 1 5 1
 6 2 7 4 2 3 5 6 4 3 7 1 5 1
 7 2 4 5 2 6 3 4 7 5 3 1 6 1
 5 7 2 6 3 2 5 4 3 7 6 1 4 1
 7 3 6 2 5 3 2 4 7 6 5 1 4 1
 3 7 4 6 3 2 5 4 2 7 6 1 5 1
 3 5 7 4 3 6 2 5 4 2 7 1 6 1
 5 3 6 4 7 3 5 2 4 6 2 1 7 1
 4 6 3 5 7 4 3 2 6 5 2 1 7 1

but the last 15 are just the reverses of the first 15.