The problem essentially concerns logograms/ideograms.
Two codes are involved in the problem. The first is the 5-digit decimal code used to render Chinese characters in Unicode.
In that system; 19968=(one), 22235=(four), 20108=(two), 19977=(three), 20845=(six), and 20116=(five), where the numbers in brackets are Chinese characters.
These can instantly be decoded by entering 'unicode xxxxx' e.g. for 19968, here:
For a crib sheet of the numerals, see:
The second code harks back to the title.
The shortest telegram exchange in the English language was between the writer Oscar Wilde and his publisher. While living in Paris, Wilde cabled his publisher in Britain to see how his new book was doing. The message read: '?'. The publisher cabled back: '!'.
Hence, since the output from the first decoding was Chinese characters, we should be seeking a way of sending those characters by telegram.
The answer is the Chinese Telegraph Code, a 4-digit code for transmitting messages written in Chinese. There is a simple decoder here:
0063=(5), 0362=(6): it follows that we are looking for the CTC encoding of (one) (which character we can Google, if necessary) which gives us the answer: 0001, thus solving the last sum and the problem.