The Rhodesia solution is used when one finds one in a dilemma situation where one would have to inform a superior (e.g. to apprise them of a scandal), but one rather did not. In fact, in the situation both informing and not informing have detrimental consequences. The Rhodesia solution is a way to inform one's superior in a way that one is not part of a cover up, while not making public the scandal at hand.
Usage in Yes, Minister
The term was popularised by the BBC's comedy series Yes Minister, more precisely, the term first arose in The Whisky Priest episode. Link to this part of the episode on YouTube
Warning, contains spoilers on the episode!
The situation in the episode is as follows (I refer to the Wikipedia page for reference of the plot):
a minister of Her Majesty's Government is visited by an army officer. The officer divulges to the minister via registered mail information regarding a terrorist group supplied with British bomb detonators. The minister is now in a position where he knows of a scandal (the Brits supplying terrorists with bomb making materials) and is aware that the army officer can prove the minister is aware (because of the recorded delivery).
The minister goes on to discuss this in his inner circle (his private secretary and the permanent secretary to the ministry), they see the dilemma: if the minister goes public or informs the PM their party would be faced with an inquiry (which may hurt their party), if he keeps quiet, the army officer will go public and divulge that the minister was aware of the situation all along.
It is at this point that the private secretary comes with the plan: the Rhodesia solution, tell the PM (Prime Minister) without actually telling the PM. This is done by sending the PM a letter*, informing him of the situation, the letter should not be alarming and the letter is to be sent when the PM is overseas, so as to cast doubt on who opens the letter.
Wikipedia says of the letter, quoting the actual episode:
" 'certain irregularities under section 1 of the Import-Export and Customs Powers (Defence) Act 1939', followed with statements that someone else do something about it and that even if they did, they would find little of relevance."
Etymology, before the Yes, Minister
In the Yes, Minister episode, Sir Humphrey, the permanent secretary explains the term refers to British oil sanctions. He says:
"A member of the government was told about the way British companies were sanction busting"
I always assumed this was fictional, made up by the writers of the series, however, this does not seem to be the case. The episode first aired on 16 December 1982, years earlier, there were actually economic sanctions in place against Rhodesia, which were actually broken by British oil companies. I will add supporting evidence in the coming paragraphs.
News reports on the cover-up:
TWP in September 1978 (quoted from the article):
Heading: British Cover-Up Charged on Oil Flow to Rhodesia
quotes from body:
This quote describes the situation in general:
"A British government inquiry disclosed yesterday that two major British oil companies broke the economic sanctions against Rhodesia and that the labor Party government of Harold Wilson was aware of the violations."
The following quote from lawyer Bingham, who was head of the public enquiry into alleged breaches of UN sanctions by oil companies in Southern Rhodesia describes a situation which fits well, if not perfectly, the situation of the word Rhodesia solution:
"In the event, both HMG and the top management of the Groups, save for limited periods, were ignorant of facts which should have been the subject certainy[sic] of consideration and possibly of action. This ignorance led HMG and the top management of the (Groups) unwittingly to make statements and give assurances which they would not have done will fully knowledge of the facts."
Reports on the subject by other news outlets:
Examples in this millennium
With explicit reference to the Yes, Minister series in their statement using the term :
A recent example of someone linking and MP's (now minister) conduct to the Rhodesia solution:
"I wonder if David Davies employed the Rhodesia Solution when he wrote his letter?"
Some examples of the term in tweets:
"The rhodesia solution. This series was way ahead of its time or way too complicit with the daily workings of a disfunctional government", by A. Raman via link
"A bit like the Rhodesia solution in Yes Minister, where you were tell the PM that Red Brigade terrorists were getting high tech British weaponry with out saying that directly. He asked but in such a way that could not be deemed to be a direct request.", by N. Triggs via link
"Not sure why I keep watching 'The Rhodesia Solution' after appearing at this week's #edinburghtraminquiry", by D. Anderson via link
"The Rhodesia Solution - Yes Minister [YouTube link] | No[sic] so much of a solution when the #DUP actually read you Memo though, is it #TheresaMay ? Total #Brexitshambles", by D. Johnson, via link
"could have used Rhodesia solution but I bet he didn't watch #YesMinister", J. Edmon in replying to another tweet via link
"The Rhodesia Solution - Yes Minister. Love this. How many times has this been used in politics?", by frazzle on Twitter via link
Without explicit reference to the Yes, Minister series in their statement using the term, but including a link to the clip:
""The #Rhodesia Solution"! I have a feeling this may have been the inspirstion[sic] for delivery of the 58 sectoral #brexit reports to Parliament by the (now) allegedly absent David Davis! ;)", by user on Twitter via link
"Good heavens, your article suggests the Civil Service still use the Rhodesia Solution occasionally", by P. G. via link
"...and the #Rhodesia Solution will apply just in case action is taken and exposed. [YouTube link] [Referencing other Twitter users]", by Twitter user via link
"Quite obvious what to do about brexit - use the Rhodesia solution", by Mike via link
"This is not complacency. This is complicity. Do not forget the Rhodesia Solution. [mentioning other Twitter user]", in reply to another tweet, by Twitter user via link
"HA[sic] this is the Rhodesia Solution. Ppl[sic] covering their asses + reassigning blame. #VanRE", in reply to another tweet, by Twitter user via link
"Email ruins everything. Not even the Rhodesia Solution is possible any more.", by A.G. Gibson via link
"In light of letters to Ministers re concerning developments I'm reminded of the "Rhodesia solution" [Youtube Link] … #callinan #vinb", by J. Doorley via link
Without any explicit reference to the Yes, Minister series in their statement using the term:
All of those are tweets:
"This is beginning to get more and more like the Rhodesia solution #Shatter", by S. Devine via link
"…between the Vreenak solution, the Rhodesia solution, and a 7% solution lies my final solution. …against humanity! …where's that coffee??", by Twitter user via link
"See Eastenders is going for the 'Rhodesia solution' while the Olympics is on", by Twitter user via link
"Yes, it's a deliberately orchestrated "communication breakdown" MT @Billablog Does anyone remember the Rhodesia Solution? #notw", by M. Groves via link