A Puzzle Of Nothing But Hats is a puzzle of Layton's Mystery Journey: Real World Puzzle Solving.



Count the amount of times each letter is present in the square:

A 7
B 6
C 3
D 2
E 11
L 9
O 21
P 5
R 9
S 1
T 8
U 4
W 13

Now you can see that C U P indeed corresponds to 3 4 5

So, similarly, 6 7 8 will correspond to B A T

The answer is BAT.

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