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# 2 letter words

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## Question

On a standard qwerty keyboard, how many "2-letter adjacency words" can be formed?

Adjacent implies that the word must be formed by two distinct letters that are next to each other on a keyboard (corners count)

Any two letters, for the sake of argument, form a two-letter word.

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• Solution

Actually, I'm going to have to amend my answer to the revised answer of:

110

because I left out the obvious dual combinations.

******  Actually, bonanova, your keyboard, I'm sure, does not look quite like that.  For instance, the "Q" key

is not perfectly adjacent diagonally to the "S" key.  And, for instance, the "W" key is not perfectly adjacent diagonally

to the "D" key.

To go from Q to S in the shortest path, you must pass through either A or W.

And to go from W to D in the shortest path, you must pass through either S or E.

You just look more closely and you'll see that the top row is not in line with the middle row, I'm sure.

Edited by Perhaps check it again
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Only A-Z characters?

What does "corners count" mean?

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Only A-Z characters?

What does "corners count" mean?

corners count means that diagonal adjacency is permitted.

And yes, only letter characters.

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bottom row --> 6

middle row --> 8

top row -------> 9

bottom row to middle row --> 14

middle row to top row -------> 18

--------------------------------------------

6 + 8 + 9 + 14 + 18 = 55

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126

My keyboard looks like this.

q w e r t y u i o p
a s d f g h j k l
z x c v b n m

Because of the offset of the bottom row from the other two, there are only diagonal pairs.

Between the top and middle rows there are orthogonal and diagonal pairs.

Thus:

top row (18):

qw we er rt ty yu ui io op po

oi iu uy yt tr re ew wq

top-middle row (52):

qa qs aq aw wa ws wd sq sw se

es ed ef dw de dr rd rf rg fe

fr ft tf tg th gr gt gy yg yh

yj ht hy hu uh uj uk jy ju ji

ij ik il ku ki ko ok ol li lo

lp pl

middle row (16):

as sd df fg gh hj jk kl lk kj

jh hg gf fd ds sa

middle- bottom row (28):

az za zs sz sx xs xd dx dc cd

cf fc fv vf vg gv gb bg bh hb

hn nh nj jn jm mj mk km

bottom row (12):

zx xc cv vb bn nm mn nb bv vc

cx xz

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