# Wordle 1056, May 10, 2024

I completed Wordle 1,056 without any mechanical or computational help. I believe I can deduce the answer from my third guess.

If you inspect the above image, after my third guess,
you see that I have all five letters.
My third guess wasn’t the best in that it doesn’t include an `e`

.
These are the facts about the letters in the answer:

`i`

occurs in column 4`a`

occurs in one of columns 2 or 5`d`

occurs in one of columns 3 or 5`m`

occurs in one of columns 1 or 2`e`

occurs in one of columns 1 or 2

I think these interact such that I can derive the answer.

Fact (2), `a`

in one of columns 2 or 5,
gives me two possibilities, combined with fact (1):

- (1.1)
`_a_i_`

- (1.2)
`___ia`

Fact (3), `d`

occurs in one of columns 3 or 5, interacts with (1.1) and (1.2).
There’s not 4 possibilities after applying fact (3), just 3.

- (1.1.1)
`_adi_`

- (1.1.2)
`_a_id`

- (1.2.1)
`__dia`

The same sort of thing happens when we apply fact (4).
Statements (1.1.1) and (1.1.2) have an `a`

in column 2,
so each of them have only one descendant after applying fact (4).

- (1.1.1.1)
`madi_`

- (1.1.2.1)
`ma_id`

- (1.2.1.1)
`m_dia`

- (1.2.1.2)
`_mdia`

Fact (5) actually eliminates any descendants of (1.1.1.1) or (1.1.2.1),
since those two statements have an `a`

in column 2, and an `m`

in column 1

- (1.2.1.1.1)
`media`

- (1.2.1.2.1)
`emdia`

Those are the only two strings that can be derived from facts (1) through (5).
`emdia`

isn’t a Wordle solution word,
so the answer is `media`

.

More graphically, the reasoning goes like this: