From The Sunday Times, 6th June 1971 [link]
There were six. Messrs. Butcher, Carpenter, Draper, Farmer, Grocer and Miller, who shared the fire-watching on Friday nights — three this week, three the next. By occupation they were (not necessarily respectively) a butcher, a carpenter, a draper, a farmer, a grocer and a miller.
Incidents were few and far between, until that Saturday morning when they found the “log” book signed by the Acting Deputy Assistant something or other, as follows: “All three present and fast asleep”.
Something had to be done about it: they decided to watch, to play whist, and to keep awake in the future. It was arranged thus: four did duty this week, next week two stood down and two others came in, and so on. Each did two turns in three weeks.
On the first Friday the carpenter, the draper, the farmer and the miller watched. Next week Mr Carpenter, Mr Draper, Mr Farmer and Mr Grocer played. On the third occasion Mr Butcher played against Mr Grocer, Mr Farmer against the butcher, and the miller against the draper. Each night the four cut for partners and kept them till morning.
If Mr Carpenter’s occupation is the same as the name of the one whose occupation is the same as the name of the one whose occupation is the same as the one whose occupation is the same as the name of the miller:
What is Mr Miller’s occupation?
As presented this puzzle has no solutions. In the comments I give a revised version that does have a unique answer.
This puzzle was originally published with no title.
[teaser521]
GeoffR and 
Frits, 
John Crabtree and 
Robert Brown are discussing. 
S2T2 
Jim Randell 8:32 am on 5 July 2020 Permalink |
Each “special seven” number corresponds to a “special one” number, which can be derived by dividing by 7.
So if we find a collection of special sevens that sum to 1, there is a corresponding set of special ones that sum to 1/7.
The decimal expansion of 1/7 = 0.(142857)…
Which if we write it as a sum of special ones will require at least 8 of them to construct the 8 digit.
Solution: The smallest number of special sevens that sum to 1 is 8.
We can construct a collection of 8 special ones that sum to 1/7 as follows:
(This is not the only set, the 0’s and 1’s in each column can be re-ordered to give other sets, and there is no reason why each recurring section should use the same arrangement of columns).
Writing these as fractions (from [a] to [h]) we have:
Which sum to: 142857/999999 = 1/7 as required.
Multiplying these values by 7 gives us a set of 8 special sevens that sum to 1:
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