As usual, Bart is correct!.
Indeed, there is a mistake in the explanation (but fortunately not in the challenge itself):
The example should be:
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Suppose the word is "suggest". You arrange the letters in
alphabetical order and number them. For the same letter, the first
occurrence will be assigned a lower number than the second
occurrence, and so on.
E is the lowest, so its number will be 1.
G is the second lowest. So the first G will be given a number 2. For
the second G, we can't use again 2, so we will assign it 3.
S is the next lowest letter. There are two occurrences of S, they
will be assigned the numbers 4, 5.
The next letter in alphabetical order is T. I is assigned the number 6.
U is the highest letter. It is assigned 7.
So "suggest" translates to 4,7,2,3,1,5,6, and its literal equivalent DGBCAEF
Unfortunately, there is no well defined process to convert a
numeric/literal key back to its original phrase/expression/keyword.
Also, there can be several words and expressions which map to the
same key. For example, "runners", "ruppert" and
"luciano" all produce the same "DGBCAEF" key (which was
derived from "suggest").
It is advised to use the following link to check your conversion:
http://rumkin.com/tools/cipher/coltrans-double.php
Select the option: "Key Word(s) - Duplicates numbered forwards" (instead of "Numeric Key - Spaced Numbers")
type in the word or sentence (no space), and the numeric equivalent is displayed below).
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Bart, thank you for your sharp eye, do not hesitate to point out any mistake, even if only in the examples.
George (the author)