Ken's Puzzle of the Week

Daisy Chains


           
           
           
           
           
           

Place the eight numbers 1 to 8 into the 6x6 grid, such that at least one number appears in each row and column. Draw a single closed path through all squares (moving up, down, left or right).  After passing through a number, the length of the path must be equal to that number when reaching the next number.  The numbers must be visited in numerical order, returning to the "1" eight squares after visiting the "8".  For example, the "5" will be visited exactly four squares after the "4".  Other than the "1" adjacent to the "2", no numbers may be in neighboring squares, not even diagonally.

Source: Original.

Solutions were received from Alan O'Donnell, Kirk Bresniker, Philippe Fondanaiche, and Nyles Heise.  There are fourteen ways to create such a chain, using nine possible configurations of the numbers 1-8.  Different paths can be found with some configurations.  There are only 6 configurations which lead to a unique path.  The solutions below are from Nyles Heise.

abcdef  12.3..
JIjihg  .....4
GHklmn  ..5...
FEDqpo  ....6.
ABCrst  ..8...
zyxwvu  ....7.
             
abcdef  12.3..
JIjihg  .....4
GHklqr  ..5...
FEDmps  ....6.
ABCnot  ..8...
zyxwvu  ....7.
             
abcdef  12.3..   Unique
Jmlihg  .....4
Inkjwx  ..5...
Horsvy  ....7.
Gpqtuz  .6....
FEDCBA  ...8..
             
abcdef  12.3..   Unique
Jyxwhg  .....4
Izuvij  ...7..
HAtslk  .....5
GBCrmn  ..8...
FEDqpo  ....6.
             
abcdef  12.3..   Unique
JIBAhg  .....4
GHCzij  ..8...
FEDylk  .....5
uvwxmn  .7....
tsrqpo  ....6.
             
abcdef  12.3..   Unique
JAzyxg  .....4
IBuvwh  ...7..
HCtsji  .8....
GDqrkl  ....5.
FEponm  ..6...
             
abcdef  12.3..   Unique
Jutsrg  .....4
Ivwxqh  .7....
HAzypi  ....6.
GBCnoj  ..8...
FEDmlk  .....5
             
wxabcd  ..12.3   Unique
vyJIfe  7.....
uzAHgh  ....4.
tCBGji  .8....
sDEFkl  ....5.
rqponm  ..6...
             
EFGdef  ...3..
DIHchg  .....4
CJabij  8.12..
Bonmlk  .....5
Apqrst  .6....
zyxwvu  ....7.
             
GHIdef  ...3..
FEJchg  .....4
CDabij  8.12..
Bonmlk  .....5
Apqrst  .6....
zyxwvu  ....7.
             
EFGdef  ...3..
DIHchg  .....4
CJabij  8.12..
Butslk  .....5
Avwrmn  .7....
zyxqpo  ....6.
             
GHIdef  ...3..
FEJchg  .....4
CDabij  8.12..
Butslk  .....5
Avwrmn  .7....
zyxqpo  ....6.
             
EFGdef  ...3..
DIHchg  .....4
CJabij  8.12..
BAzylk  .....5
uvwxmn  .7....
tsrqpo  ....6.
             
GHIdef  ...3..
FEJchg  .....4
CDabij  8.12..
BAzylk  .....5
uvwxmn  .7....
tsrqpo  ....6.
 

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