Latin Squares for Constructing "Williams Designs" - Balanced for First-order Carry-over (Residual) Effects

Courtesy from the website http://statpages.info/latinsq.html, the list below contains the Williams design with 2 to 26 treatment groups. It is unlikely to have a clinical trial with 26 treatment groups. The most number of treatment groups I see is a study with 6 treatment groups. 

In one of my previous posts, I described the Williams design and its usefulness in phase I or clinical pharmacology studies. In a SAS SUGI paper "Generating Randomization Schedules Using SAS Programming", I described how to use SAS program to construct the randomization schedule for a study with Williams design. 

With the limited sample size, the Williams design is the most efficient design and minimizes the potential impact of the carryover effect. In Williams design with an even number of n treatment groups, there will be n number of sequences or an "n by n" square. Each treatment only occurs one time in one sequence, in one period. Furthermore, each treatment only follows another treatment one time. 

If the number of treatments (n) is an odd number, there will be 2 x n number of sequences or two n by n squares. Each treatment only occurs once in one sequence and in two periods. Each treatment only follows another treatment twice. 

With the Latin Square listed below, we can easily construct the crossover design with treatments, periods, and sequences. For example, a study design with 3 treatment groups will have the following assignments: three treatment groups (A, B, C), three periods (period 1, period 2, and period 3), and six sequences (ABC, BCA, CAB, CBA, ACB, and BAC). 

Treatment Sequence	Period 1	Period 2	Period 3
1	A	B	C
2	B	C	A
3	C	A	B
4	C	B	A
5	A	C	B
6	B	A	C

• Since it is the crossover design, there should be a washout period between each period. It is very common that the washout period is 5 times the half-life. 
• Randomization is for the sequence, not the treatment group. 
• Once we know the number of subjects is needed for each sequence, we will know the total number of subjects for the entire study. 
• Usually, the mixed model is needed for statistical analysis. The statistical model will need to consider the treatment, period, and sequence. An example of the SAS codes for analysis was provided in one of the previous posts "Cookbook SAS Codes for Bioequivalence Test in 2x2x2 Crossover Design"

Williams Design by the Number of Treatment Groups:

Size = 2

A B 
B A 
 

Size = 3

A B C 
B C A 
C A B 
C B A 
A C B 
B A C 
 

Size = 4

A B D C 
B C A D 
C D B A 
D A C B 
 

Size = 5

A B E C D 
B C A D E 
C D B E A 
D E C A B 
E A D B C 
D C E B A 
E D A C B 
A E B D C 
B A C E D 
C B D A E 
 

Size = 6

A B F C E D 
B C A D F E 
C D B E A F 
D E C F B A 
E F D A C B 
F A E B D C 
 

Size = 7

A B G C F D E 
B C A D G E F 
C D B E A F G 
D E C F B G A 
E F D G C A B 
F G E A D B C 
G A F B E C D 
E D F C G B A 
F E G D A C B 
G F A E B D C 
A G B F C E D 
B A C G D F E 
C B D A E G F 
D C E B F A G 
 

Size = 8

A B H C G D F E 
B C A D H E G F 
C D B E A F H G 
D E C F B G A H 
E F D G C H B A 
F G E H D A C B 
G H F A E B D C 
H A G B F C E D 
 

Size = 9

A B I C H D G E F 
B C A D I E H F G 
C D B E A F I G H 
D E C F B G A H I 
E F D G C H B I A 
F G E H D I C A B 
G H F I E A D B C 
H I G A F B E C D 
I A H B G C F D E 
F E G D H C I B A 
G F H E I D A C B 
H G I F A E B D C 
I H A G B F C E D 
A I B H C G D F E 
B A C I D H E G F 
C B D A E I F H G 
D C E B F A G I H 
E D F C G B H A I 
 

Size = 10

A B J C I D H E G F 
B C A D J E I F H G 
C D B E A F J G I H 
D E C F B G A H J I 
E F D G C H B I A J 
F G E H D I C J B A 
G H F I E J D A C B 
H I G J F A E B D C 
I J H A G B F C E D 
J A I B H C G D F E 
 
 
Size = 11

A B K C J D I E H F G 
B C A D K E J F I G H 
C D B E A F K G J H I 
D E C F B G A H K I J 
E F D G C H B I A J K 
F G E H D I C J B K A 
G H F I E J D K C A B 
H I G J F K E A D B C 
I J H K G A F B E C D 
J K I A H B G C F D E 
K A J B I C H D G E F 
G F H E I D J C K B A 
H G I F J E K D A C B 
I H J G K F A E B D C 
J I K H A G B F C E D 
K J A I B H C G D F E 
A K B J C I D H E G F 
B A C K D J E I F H G 
C B D A E K F J G I H 
D C E B F A G K H J I 
E D F C G B H A I K J 
F E G D H C I B J A K 
 

Size = 12

A B L C K D J E I F H G 
B C A D L E K F J G I H 
C D B E A F L G K H J I 
D E C F B G A H L I K J 
E F D G C H B I A J L K 
F G E H D I C J B K A L 
G H F I E J D K C L B A 
H I G J F K E L D A C B 
I J H K G L F A E B D C 
J K I L H A G B F C E D 
K L J A I B H C G D F E 
L A K B J C I D H E G F 
 
 
Size = 13

A B M C L D K E J F I G H 
B C A D M E L F K G J H I 
C D B E A F M G L H K I J 
D E C F B G A H M I L J K 
E F D G C H B I A J M K L 
F G E H D I C J B K A L M 
G H F I E J D K C L B M A 
H I G J F K E L D M C A B 
I J H K G L F M E A D B C 
J K I L H M G A F B E C D 
K L J M I A H B G C F D E 
L M K A J B I C H D G E F 
M A L B K C J D I E H F G 
H G I F J E K D L C M B A 
I H J G K F L E M D A C B 
J I K H L G M F A E B D C 
K J L I M H A G B F C E D 
L K M J A I B H C G D F E 
M L A K B J C I D H E G F 
A M B L C K D J E I F H G 
B A C M D L E K F J G I H 
C B D A E M F L G K H J I 
D C E B F A G M H L I K J 
E D F C G B H A I M J L K 
F E G D H C I B J A K M L 
G F H E I D J C K B L A M 
 
 
Size = 14

A B N C M D L E K F J G I H 
B C A D N E M F L G K H J I 
C D B E A F N G M H L I K J 
D E C F B G A H N I M J L K 
E F D G C H B I A J N K M L 
F G E H D I C J B K A L N M 
G H F I E J D K C L B M A N 
H I G J F K E L D M C N B A 
I J H K G L F M E N D A C B 
J K I L H M G N F A E B D C 
K L J M I N H A G B F C E D 
L M K N J A I B H C G D F E 
M N L A K B J C I D H E G F 
N A M B L C K D J E I F H G 
 
 
Size = 15

A B O C N D M E L F K G J H I 
B C A D O E N F M G L H K I J 
C D B E A F O G N H M I L J K 
D E C F B G A H O I N J M K L 
E F D G C H B I A J O K N L M 
F G E H D I C J B K A L O M N 
G H F I E J D K C L B M A N O 
H I G J F K E L D M C N B O A 
I J H K G L F M E N D O C A B 
J K I L H M G N F O E A D B C 
K L J M I N H O G A F B E C D 
L M K N J O I A H B G C F D E 
M N L O K A J B I C H D G E F 
N O M A L B K C J D I E H F G 
O A N B M C L D K E J F I G H 
I H J G K F L E M D N C O B A 
J I K H L G M F N E O D A C B 
K J L I M H N G O F A E B D C 
L K M J N I O H A G B F C E D 
M L N K O J A I B H C G D F E 
N M O L A K B J C I D H E G F 
O N A M B L C K D J E I F H G 
A O B N C M D L E K F J G I H 
B A C O D N E M F L G K H J I 
C B D A E O F N G M H L I K J 
D C E B F A G O H N I M J L K 
E D F C G B H A I O J N K M L 
F E G D H C I B J A K O L N M 
G F H E I D J C K B L A M O N 
H G I F J E K D L C M B N A O 
 

Size = 16

A B P C O D N E M F L G K H J I 
B C A D P E O F N G M H L I K J 
C D B E A F P G O H N I M J L K 
D E C F B G A H P I O J N K M L 
E F D G C H B I A J P K O L N M 
F G E H D I C J B K A L P M O N 
G H F I E J D K C L B M A N P O 
H I G J F K E L D M C N B O A P 
I J H K G L F M E N D O C P B A 
J K I L H M G N F O E P D A C B 
K L J M I N H O G P F A E B D C 
L M K N J O I P H A G B F C E D 
M N L O K P J A I B H C G D F E 
N O M P L A K B J C I D H E G F 
O P N A M B L C K D J E I F H G 
P A O B N C M D L E K F J G I H 
 

Size = 17

A B Q C P D O E N F M G L H K I J 
B C A D Q E P F O G N H M I L J K 
C D B E A F Q G P H O I N J M K L 
D E C F B G A H Q I P J O K N L M 
E F D G C H B I A J Q K P L O M N 
F G E H D I C J B K A L Q M P N O 
G H F I E J D K C L B M A N Q O P 
H I G J F K E L D M C N B O A P Q 
I J H K G L F M E N D O C P B Q A 
J K I L H M G N F O E P D Q C A B 
K L J M I N H O G P F Q E A D B C 
L M K N J O I P H Q G A F B E C D 
M N L O K P J Q I A H B G C F D E 
N O M P L Q K A J B I C H D G E F 
O P N Q M A L B K C J D I E H F G 
P Q O A N B M C L D K E J F I G H 
Q A P B O C N D M E L F K G J H I 
J I K H L G M F N E O D P C Q B A 
K J L I M H N G O F P E Q D A C B 
L K M J N I O H P G Q F A E B D C 
M L N K O J P I Q H A G B F C E D 
N M O L P K Q J A I B H C G D F E 
O N P M Q L A K B J C I D H E G F 
P O Q N A M B L C K D J E I F H G 
Q P A O B N C M D L E K F J G I H 
A Q B P C O D N E M F L G K H J I 
B A C Q D P E O F N G M H L I K J 
C B D A E Q F P G O H N I M J L K 
D C E B F A G Q H P I O J N K M L 
E D F C G B H A I Q J P K O L N M 
F E G D H C I B J A K Q L P M O N 
G F H E I D J C K B L A M Q N P O 
H G I F J E K D L C M B N A O Q P 
I H J G K F L E M D N C O B P A Q 
 
 

Size = 18

A B R C Q D P E O F N G M H L I K J 
B C A D R E Q F P G O H N I M J L K 
C D B E A F R G Q H P I O J N K M L 
D E C F B G A H R I Q J P K O L N M 
E F D G C H B I A J R K Q L P M O N 
F G E H D I C J B K A L R M Q N P O 
G H F I E J D K C L B M A N R O Q P 
H I G J F K E L D M C N B O A P R Q 
I J H K G L F M E N D O C P B Q A R 
J K I L H M G N F O E P D Q C R B A 
K L J M I N H O G P F Q E R D A C B 
L M K N J O I P H Q G R F A E B D C 
M N L O K P J Q I R H A G B F C E D 
N O M P L Q K R J A I B H C G D F E 
O P N Q M R L A K B J C I D H E G F 
P Q O R N A M B L C K D J E I F H G 
Q R P A O B N C M D L E K F J G I H 
R A Q B P C O D N E M F L G K H J I 
 

Size = 19

A B S C R D Q E P F O G N H M I L J K 
B C A D S E R F Q G P H O I N J M K L 
C D B E A F S G R H Q I P J O K N L M 
D E C F B G A H S I R J Q K P L O M N 
E F D G C H B I A J S K R L Q M P N O 
F G E H D I C J B K A L S M R N Q O P 
G H F I E J D K C L B M A N S O R P Q 
H I G J F K E L D M C N B O A P S Q R 
I J H K G L F M E N D O C P B Q A R S 
J K I L H M G N F O E P D Q C R B S A 
K L J M I N H O G P F Q E R D S C A B 
L M K N J O I P H Q G R F S E A D B C 
M N L O K P J Q I R H S G A F B E C D 
N O M P L Q K R J S I A H B G C F D E 
O P N Q M R L S K A J B I C H D G E F 
P Q O R N S M A L B K C J D I E H F G 
Q R P S O A N B M C L D K E J F I G H 
R S Q A P B O C N D M E L F K G J H I 
S A R B Q C P D O E N F M G L H K I J 
K J L I M H N G O F P E Q D R C S B A 
L K M J N I O H P G Q F R E S D A C B 
M L N K O J P I Q H R G S F A E B D C 
N M O L P K Q J R I S H A G B F C E D 
O N P M Q L R K S J A I B H C G D F E 
P O Q N R M S L A K B J C I D H E G F 
Q P R O S N A M B L C K D J E I F H G 
R Q S P A O B N C M D L E K F J G I H 
S R A Q B P C O D N E M F L G K H J I 
A S B R C Q D P E O F N G M H L I K J 
B A C S D R E Q F P G O H N I M J L K 
C B D A E S F R G Q H P I O J N K M L 
D C E B F A G S H R I Q J P K O L N M 
E D F C G B H A I S J R K Q L P M O N 
F E G D H C I B J A K S L R M Q N P O 
G F H E I D J C K B L A M S N R O Q P 
H G I F J E K D L C M B N A O S P R Q 
I H J G K F L E M D N C O B P A Q S R 
J I K H L G M F N E O D P C Q B R A S 
 

Size = 20

A B T C S D R E Q F P G O H N I M J L K 
B C A D T E S F R G Q H P I O J N K M L 
C D B E A F T G S H R I Q J P K O L N M 
D E C F B G A H T I S J R K Q L P M O N 
E F D G C H B I A J T K S L R M Q N P O 
F G E H D I C J B K A L T M S N R O Q P 
G H F I E J D K C L B M A N T O S P R Q 
H I G J F K E L D M C N B O A P T Q S R 
I J H K G L F M E N D O C P B Q A R T S 
J K I L H M G N F O E P D Q C R B S A T 
K L J M I N H O G P F Q E R D S C T B A 
L M K N J O I P H Q G R F S E T D A C B 
M N L O K P J Q I R H S G T F A E B D C 
N O M P L Q K R J S I T H A G B F C E D 
O P N Q M R L S K T J A I B H C G D F E 
P Q O R N S M T L A K B J C I D H E G F 
Q R P S O T N A M B L C K D J E I F H G 
R S Q T P A O B N C M D L E K F J G I H 
S T R A Q B P C O D N E M F L G K H J I 
T A S B R C Q D P E O F N G M H L I K J 
 

Size = 21

A B U C T D S E R F Q G P H O I N J M K L 
B C A D U E T F S G R H Q I P J O K N L M 
C D B E A F U G T H S I R J Q K P L O M N 
D E C F B G A H U I T J S K R L Q M P N O 
E F D G C H B I A J U K T L S M R N Q O P 
F G E H D I C J B K A L U M T N S O R P Q 
G H F I E J D K C L B M A N U O T P S Q R 
H I G J F K E L D M C N B O A P U Q T R S 
I J H K G L F M E N D O C P B Q A R U S T 
J K I L H M G N F O E P D Q C R B S A T U 
K L J M I N H O G P F Q E R D S C T B U A 
L M K N J O I P H Q G R F S E T D U C A B 
M N L O K P J Q I R H S G T F U E A D B C 
N O M P L Q K R J S I T H U G A F B E C D 
O P N Q M R L S K T J U I A H B G C F D E 
P Q O R N S M T L U K A J B I C H D G E F 
Q R P S O T N U M A L B K C J D I E H F G 
R S Q T P U O A N B M C L D K E J F I G H 
S T R U Q A P B O C N D M E L F K G J H I 
T U S A R B Q C P D O E N F M G L H K I J 
U A T B S C R D Q E P F O G N H M I L J K 
L K M J N I O H P G Q F R E S D T C U B A 
M L N K O J P I Q H R G S F T E U D A C B 
N M O L P K Q J R I S H T G U F A E B D C 
O N P M Q L R K S J T I U H A G B F C E D 
P O Q N R M S L T K U J A I B H C G D F E 
Q P R O S N T M U L A K B J C I D H E G F 
R Q S P T O U N A M B L C K D J E I F H G 
S R T Q U P A O B N C M D L E K F J G I H 
T S U R A Q B P C O D N E M F L G K H J I 
U T A S B R C Q D P E O F N G M H L I K J 
A U B T C S D R E Q F P G O H N I M J L K 
B A C U D T E S F R G Q H P I O J N K M L 
C B D A E U F T G S H R I Q J P K O L N M 
D C E B F A G U H T I S J R K Q L P M O N 
E D F C G B H A I U J T K S L R M Q N P O 
F E G D H C I B J A K U L T M S N R O Q P 
G F H E I D J C K B L A M U N T O S P R Q 
H G I F J E K D L C M B N A O U P T Q S R 
I H J G K F L E M D N C O B P A Q U R T S 
J I K H L G M F N E O D P C Q B R A S U T 
K J L I M H N G O F P E Q D R C S B T A U 
 


Size = 22

A B V C U D T E S F R G Q H P I O J N K M L 
B C A D V E U F T G S H R I Q J P K O L N M 
C D B E A F V G U H T I S J R K Q L P M O N 
D E C F B G A H V I U J T K S L R M Q N P O 
E F D G C H B I A J V K U L T M S N R O Q P 
F G E H D I C J B K A L V M U N T O S P R Q 
G H F I E J D K C L B M A N V O U P T Q S R 
H I G J F K E L D M C N B O A P V Q U R T S 
I J H K G L F M E N D O C P B Q A R V S U T 
J K I L H M G N F O E P D Q C R B S A T V U 
K L J M I N H O G P F Q E R D S C T B U A V 
L M K N J O I P H Q G R F S E T D U C V B A 
M N L O K P J Q I R H S G T F U E V D A C B 
N O M P L Q K R J S I T H U G V F A E B D C 
O P N Q M R L S K T J U I V H A G B F C E D 
P Q O R N S M T L U K V J A I B H C G D F E 
Q R P S O T N U M V L A K B J C I D H E G F 
R S Q T P U O V N A M B L C K D J E I F H G 
S T R U Q V P A O B N C M D L E K F J G I H 
T U S V R A Q B P C O D N E M F L G K H J I 
U V T A S B R C Q D P E O F N G M H L I K J 
V A U B T C S D R E Q F P G O H N I M J L K 
 


Size = 23

A B W C V D U E T F S G R H Q I P J O K N L M 
B C A D W E V F U G T H S I R J Q K P L O M N 
C D B E A F W G V H U I T J S K R L Q M P N O 
D E C F B G A H W I V J U K T L S M R N Q O P 
E F D G C H B I A J W K V L U M T N S O R P Q 
F G E H D I C J B K A L W M V N U O T P S Q R 
G H F I E J D K C L B M A N W O V P U Q T R S 
H I G J F K E L D M C N B O A P W Q V R U S T 
I J H K G L F M E N D O C P B Q A R W S V T U 
J K I L H M G N F O E P D Q C R B S A T W U V 
K L J M I N H O G P F Q E R D S C T B U A V W 
L M K N J O I P H Q G R F S E T D U C V B W A 
M N L O K P J Q I R H S G T F U E V D W C A B 
N O M P L Q K R J S I T H U G V F W E A D B C 
O P N Q M R L S K T J U I V H W G A F B E C D 
P Q O R N S M T L U K V J W I A H B G C F D E 
Q R P S O T N U M V L W K A J B I C H D G E F 
R S Q T P U O V N W M A L B K C J D I E H F G 
S T R U Q V P W O A N B M C L D K E J F I G H 
T U S V R W Q A P B O C N D M E L F K G J H I 
U V T W S A R B Q C P D O E N F M G L H K I J 
V W U A T B S C R D Q E P F O G N H M I L J K 
W A V B U C T D S E R F Q G P H O I N J M K L 
M L N K O J P I Q H R G S F T E U D V C W B A 
N M O L P K Q J R I S H T G U F V E W D A C B 
O N P M Q L R K S J T I U H V G W F A E B D C 
P O Q N R M S L T K U J V I W H A G B F C E D 
Q P R O S N T M U L V K W J A I B H C G D F E 
R Q S P T O U N V M W L A K B J C I D H E G F 
S R T Q U P V O W N A M B L C K D J E I F H G 
T S U R V Q W P A O B N C M D L E K F J G I H 
U T V S W R A Q B P C O D N E M F L G K H J I 
V U W T A S B R C Q D P E O F N G M H L I K J 
W V A U B T C S D R E Q F P G O H N I M J L K 
A W B V C U D T E S F R G Q H P I O J N K M L 
B A C W D V E U F T G S H R I Q J P K O L N M 
C B D A E W F V G U H T I S J R K Q L P M O N 
D C E B F A G W H V I U J T K S L R M Q N P O 
E D F C G B H A I W J V K U L T M S N R O Q P 
F E G D H C I B J A K W L V M U N T O S P R Q 
G F H E I D J C K B L A M W N V O U P T Q S R 
H G I F J E K D L C M B N A O W P V Q U R T S 
I H J G K F L E M D N C O B P A Q W R V S U T 
J I K H L G M F N E O D P C Q B R A S W T V U 
K J L I M H N G O F P E Q D R C S B T A U W V 
L K M J N I O H P G Q F R E S D T C U B V A W 
 

Size = 24

A B X C W D V E U F T G S H R I Q J P K O L N M 
B C A D X E W F V G U H T I S J R K Q L P M O N 
C D B E A F X G W H V I U J T K S L R M Q N P O 
D E C F B G A H X I W J V K U L T M S N R O Q P 
E F D G C H B I A J X K W L V M U N T O S P R Q 
F G E H D I C J B K A L X M W N V O U P T Q S R 
G H F I E J D K C L B M A N X O W P V Q U R T S 
H I G J F K E L D M C N B O A P X Q W R V S U T 
I J H K G L F M E N D O C P B Q A R X S W T V U 
J K I L H M G N F O E P D Q C R B S A T X U W V 
K L J M I N H O G P F Q E R D S C T B U A V X W 
L M K N J O I P H Q G R F S E T D U C V B W A X 
M N L O K P J Q I R H S G T F U E V D W C X B A 
N O M P L Q K R J S I T H U G V F W E X D A C B 
O P N Q M R L S K T J U I V H W G X F A E B D C 
P Q O R N S M T L U K V J W I X H A G B F C E D 
Q R P S O T N U M V L W K X J A I B H C G D F E 
R S Q T P U O V N W M X L A K B J C I D H E G F 
S T R U Q V P W O X N A M B L C K D J E I F H G 
T U S V R W Q X P A O B N C M D L E K F J G I H 
U V T W S X R A Q B P C O D N E M F L G K H J I 
V W U X T A S B R C Q D P E O F N G M H L I K J 
W X V A U B T C S D R E Q F P G O H N I M J L K 
X A W B V C U D T E S F R G Q H P I O J N K M L 
 
 

Size = 25

A B Y C X D W E V F U G T H S I R J Q K P L O M N 
B C A D Y E X F W G V H U I T J S K R L Q M P N O 
C D B E A F Y G X H W I V J U K T L S M R N Q O P 
D E C F B G A H Y I X J W K V L U M T N S O R P Q 
E F D G C H B I A J Y K X L W M V N U O T P S Q R 
F G E H D I C J B K A L Y M X N W O V P U Q T R S 
G H F I E J D K C L B M A N Y O X P W Q V R U S T 
H I G J F K E L D M C N B O A P Y Q X R W S V T U 
I J H K G L F M E N D O C P B Q A R Y S X T W U V 
J K I L H M G N F O E P D Q C R B S A T Y U X V W 
K L J M I N H O G P F Q E R D S C T B U A V Y W X 
L M K N J O I P H Q G R F S E T D U C V B W A X Y 
M N L O K P J Q I R H S G T F U E V D W C X B Y A 
N O M P L Q K R J S I T H U G V F W E X D Y C A B 
O P N Q M R L S K T J U I V H W G X F Y E A D B C 
P Q O R N S M T L U K V J W I X H Y G A F B E C D 
Q R P S O T N U M V L W K X J Y I A H B G C F D E 
R S Q T P U O V N W M X L Y K A J B I C H D G E F 
S T R U Q V P W O X N Y M A L B K C J D I E H F G 
T U S V R W Q X P Y O A N B M C L D K E J F I G H 
U V T W S X R Y Q A P B O C N D M E L F K G J H I 
V W U X T Y S A R B Q C P D O E N F M G L H K I J 
W X V Y U A T B S C R D Q E P F O G N H M I L J K 
X Y W A V B U C T D S E R F Q G P H O I N J M K L 
Y A X B W C V D U E T F S G R H Q I P J O K N L M 
N M O L P K Q J R I S H T G U F V E W D X C Y B A 
O N P M Q L R K S J T I U H V G W F X E Y D A C B 
P O Q N R M S L T K U J V I W H X G Y F A E B D C 
Q P R O S N T M U L V K W J X I Y H A G B F C E D 
R Q S P T O U N V M W L X K Y J A I B H C G D F E 
S R T Q U P V O W N X M Y L A K B J C I D H E G F 
T S U R V Q W P X O Y N A M B L C K D J E I F H G 
U T V S W R X Q Y P A O B N C M D L E K F J G I H 
V U W T X S Y R A Q B P C O D N E M F L G K H J I 
W V X U Y T A S B R C Q D P E O F N G M H L I K J 
X W Y V A U B T C S D R E Q F P G O H N I M J L K 
Y X A W B V C U D T E S F R G Q H P I O J N K M L 
A Y B X C W D V E U F T G S H R I Q J P K O L N M 
B A C Y D X E W F V G U H T I S J R K Q L P M O N 
C B D A E Y F X G W H V I U J T K S L R M Q N P O 
D C E B F A G Y H X I W J V K U L T M S N R O Q P 
E D F C G B H A I Y J X K W L V M U N T O S P R Q 
F E G D H C I B J A K Y L X M W N V O U P T Q S R 
G F H E I D J C K B L A M Y N X O W P V Q U R T S 
H G I F J E K D L C M B N A O Y P X Q W R V S U T 
I H J G K F L E M D N C O B P A Q Y R X S W T V U 
J I K H L G M F N E O D P C Q B R A S Y T X U W V 
K J L I M H N G O F P E Q D R C S B T A U Y V X W 
L K M J N I O H P G Q F R E S D T C U B V A W Y X 
M L N K O J P I Q H R G S F T E U D V C W B X A Y 
 


Size = 26

A B Z C Y D X E W F V G U H T I S J R K Q L P M O N 
B C A D Z E Y F X G W H V I U J T K S L R M Q N P O 
C D B E A F Z G Y H X I W J V K U L T M S N R O Q P 
D E C F B G A H Z I Y J X K W L V M U N T O S P R Q 
E F D G C H B I A J Z K Y L X M W N V O U P T Q S R 
F G E H D I C J B K A L Z M Y N X O W P V Q U R T S 
G H F I E J D K C L B M A N Z O Y P X Q W R V S U T 
H I G J F K E L D M C N B O A P Z Q Y R X S W T V U 
I J H K G L F M E N D O C P B Q A R Z S Y T X U W V 
J K I L H M G N F O E P D Q C R B S A T Z U Y V X W 
K L J M I N H O G P F Q E R D S C T B U A V Z W Y X 
L M K N J O I P H Q G R F S E T D U C V B W A X Z Y 
M N L O K P J Q I R H S G T F U E V D W C X B Y A Z 
N O M P L Q K R J S I T H U G V F W E X D Y C Z B A 
O P N Q M R L S K T J U I V H W G X F Y E Z D A C B 
P Q O R N S M T L U K V J W I X H Y G Z F A E B D C 
Q R P S O T N U M V L W K X J Y I Z H A G B F C E D 
R S Q T P U O V N W M X L Y K Z J A I B H C G D F E 
S T R U Q V P W O X N Y M Z L A K B J C I D H E G F 
T U S V R W Q X P Y O Z N A M B L C K D J E I F H G 
U V T W S X R Y Q Z P A O B N C M D L E K F J G I H 
V W U X T Y S Z R A Q B P C O D N E M F L G K H J I 
W X V Y U Z T A S B R C Q D P E O F N G M H L I K J 
X Y W Z V A U B T C S D R E Q F P G O H N I M J L K 
Y Z X A W B V C U D T E S F R G Q H P I O J N K M L 
Z A Y B X C W D V E U F T G S H R I Q J P K O L N M