Step 1: Consider row 16, and recall that each row contains letters from
IDAHOSYL and no letter will be used more than once. Row 16 has only
seven hexes, so one letter won't be used. Currently, AYSO
have been used — thus the three empty hexes (19, 20, and 21) must each
use one of IDHL.
Looking at hex 21, it can’t be I because hex 14 is on
the same slanted line; and it can’t be H or
L because hexes 36 and 37 are in the same region (region 21).
Thus hex 21 is a D.
Step 2: Now consider hex 20. It can’t be I because 14 is
in the same region; and it can’t be H because 36 is on
the same slant. Thus 20 is an L.
Step 3: Similarly, 19 can’t be I because 6 is
on the same slant. Thus 19 is an H.
Step 4: Now consider the three empty hexes in region 31 (33, 44, and 45).
DIOYS have been used, so the three empty hexes must use
AHL. 33 can’t be H or
L because hexes 36 and 37 are in the same row. So 33 is
A.
Step 5: 44 can’t be H because it is on the same slant as
19. So 44 is L.
Step 6: The only letter left for 45 is H.
Step 7: Turning to region 4, hexes 4 and 9 must use AD. 4
can’t be A because of 33. So 4 is D.
Step 8: The only letter left for 9 is A.
Step 9: Next, consider the slant running from 4 to 44. Only 26 is empty, and
DSOHAYL have been used. The only letter left is
I, so 26 is I.
Step 10: Now for region 21. 28, 29, 30, and 43 must use IASY.
30 can’t be I because of 26; and it can't be
A or Y because of 9 and 15.
So 30 is S.
Step 11: 28 can’t be I because of 26; and it can't be
Y because of 15. So 28 is A.
Step 12: 29 can’t be I because of 26, so 29 is
Y.
Step 13: The only letter left for 43 is I.
Step 14: In row 23, 23, 24, 25, and 27 must use HDOL. 23
can’t be D, O, or L
because of 31, 38, and 44. So 23 is H.
Step 15: 24 can’t be D or L because of
31 and 11. So 24 is O.
Step 16: 27 can’t be L because of 20. So 27 is
D.
Step 17: The only letter left for 25 is L.
Step 18: At this point we know the hidden message spelled out along row 23
— HOLIDAYS. But we can easily fill the remaining hexes
in the puzzle. Region 10 is complete except for 10, which has to be
D.
Step 19: We see that 12 is the only empty hex in row 10. Row 10 has only six
hexes, so two letters won't be used. DLOIY have been used, so
12 must be one of AHS. But it can’t be
H because of 19 and it can’t be S
because of 18. So 12 is A.
Step 20: For region 1, hexes 1, 2, 3, and 7 must use DHSY.
The D at 4 prevents 1, 2, or 3 from being
D. So 7 must be D.
Step 21: The Hs at 19 and 36 prevent 1 or 2 from being
H. So 3 must be H.
Step 22: The Y at 17 prevents 2 from being
Y. So 1 must be Y.
Step 23: The only letter left for 2 is S.
Step 24: For region 27, hexes 35, 42, 46, 47, and 48 must use
IAOSL. The Is at 26 and 6 prevent all but 46
from being I. So 46 must be I.
Step 25: The Ls at 44 and 37 prevent all but 42 from being
L. So 42 must be L.
Step 26: The A at 12 prevents 35 and 48 from being
A. So 47 must be A.
Step 27: 48 must be one of OS but 30 is an S.
So 48 must be O.
Step 28: The only letter left for 35 is S.
Step 29: And so here we have the full solution.
