When Decoded the original message hidden in the transposition cipher reads like this: 'The rabbit hole went straight on like a tunnel for some way and then dipped suddenly down so suddenly that Alice had not a moment to think about stopping herself before she found herself falling down what seemed to be a very deep well' This is a quote from the book 'Alice's Adventures in Wonderland' By Lewis Caroll.
To work this out I used the same method shown in the example for the problem. The Encoded message given was: 'ttanopnshonstpdeendoaiherltsmnemaihuogrebkedmhsdbendeeetiadenrlottin
tsfbhupltefeonpyolaalnettflveedhhblewlsaieirefutnfnynodakogdtrdlarde
sseibeoetoncoswprmleuhnwaeyhteweiwdasfhlgaodtoalhywnoutx' You may notice that this has one extra character not used in the original message, as in the example padding characters were added, in this case just one 'x' was used; this is to make decoding the message slightly more difficult. In the example (a quote from 'Peter rabbit' by Beatrix Potter) the original message contains 44 characters, however 4 extra padding characters were added; although you can make a grid with 44 characters, 48 has more factors, meaning more possible grids, making it harder to work out the original message.
The first stage of the problem was to count the amount of characters in the encoded message, in this case there were 192 charecters.
The next thing I did was to find all the possible sets of factors of 192. By working out the positive integers that multiply together to make 192, because these are the grids that the letters will be arranged into, I am counting for example 1x192 and 192x1 as different, however for this particular pair that will make no difference with others it will:
1 x 192
2 x 96
3 x 64
4 x 48
6 x 32
8 x 24
12 x 16
16 x 12
24 x 8
32 x 6
48 x 4
64 x 3
96 x 2
192 x 1
These are all 14 possible grids that can be made with 192 characters, although it is unlikely that all of them will need to be tried before the answer is found.
After finding all possible grids, you can do pretty much the same as the example and make each, reading down the columns to see if they make any sense, or are just a jumble of letters.
Here are the grids I came up with before I found the message which had been encoded, it was unnecessary to make the grids 1x192 and 192x1 as you can see how they would turn out simply by reading across the encoded message.
Unfortunately the 2x96 grid, does not fit properly on this page, but the beggining of the message you can get if you read down the columns is 'teteadnh...' obviously not English.
Ttanopnshonstpdeendoaiherltsmnemaihuogrebkedmhsdbendeeetiadenrlo
ttintsfbhupltefeonpyolaalnettflveedhhblewlsaieirefutnfnynodakogd
trdlardesseibeoetoncoswprmleuhnwaeyhteweiwdasfhlgaodtoalhywnoutx
The 3x64 grid also makes no sense.
Ttanopnshonstpdeendoaiherltsmnemaihuogrebkedmhsd
bendeeetiadenrlottintsfbhupltefeonpyolaalnettflv
eedhhblewlsaieirefutnfnynodakogdtrdlardesseibeoe
toncoswprmleuhnwaeyhteweiwdasfhlgaodtoalhywnoutx
As does the 4x48 grid...
Ttanopnshonstpdeendoaiherltsmnem
aihuogrebkedmhsdbendeeetiadenrlo
ttintsfbhupltefeonpyolaalnettflv
eedhhblewlsaieirefutnfnynodakogd
trdlardesseibeoetoncoswprmleuhnw
aeyhteweiwdasfhlgaodtoalhywnoutx
...and the 6x32 grid...
Ttanopnshonstpdeendoaihe
rltsmnemaihuogrebkedmhsd
bendeeetiadenrlottintsfb
hupltefeonpyolaalnettflv
eedhhblewlsaieirefutnfny
nodakogdtrdlardesseibeoe
toncoswprmleuhnwaeyhtewe
iwdasfhlgaodtoalhywnoutx
Ttanopnshonstpde
endoaiherltsmnem
aihuogrebkedmhsd
bendeeetiadenrlo
ttintsfbhupltefe
onpyolaalnettflv
eedhhblewlsaieir
efutnfnynodakogd
trdlardesseibeoe
toncoswprmleuhnw
aeyhteweiwdasfhl
gaodtoalhywnoutx
...The start of the 12x16 grid gives you 'tea' but then fades into nonsense language...
Ttanopnshons
tpdeendoaihe
rltsmnemaihu
ogrebkedmhsd
bendeeetiade
nrlottintsfb
hupltefeonpy
olaalnettflv
eedhhblewlsa
ieirefutnfny
nodakogdtrdl
ardesseibeoe
toncoswprmle
uhnwaeyhtewe
iwdasfhlgaod
toalhywnoutx
...the 16x12 grid makes about as much sense as all the previous ones, but...
Ttanopns
honstpde
endoaihe
rltsmnem
aihuogre
bkedmhsd
bendeeet
iadenrlo
ttintsfb
hupltefe
onpyolaa
lnettflv
eedhhble
wlsaieir
efutnfny
nodakogd
trdlarde
sseibeoe
toncoswp
rmleuhnw
aeyhtewe
iwdasfhl
gaodtoal
hywnoutx
...finally we find some English in the 24x8 grid! Reading downwards gives us the quote shown at the beginning from 'Alice's Adventures in Wonderland'. I chose not to continue with the grids as the chance that this was in fact not the intended message is so minute and the idea that this quote has in fact turned up by chance sounds verging on crazy!