**From New Scientist #1607, 7th April 1988** [link]

“Look at this four-figure temperature,” the furnace foreman said, “it’s HEAT.”

“That’s funny, the temperature of my furnace is HOTS,” said the foreman of the adjacent furnace.

As usual, I’ve replaced digits consistently with letters to confuse you, different letters being used for different digits. One of the above temperatures is on the centigrade scale and the other is on the Fahrenheit scale. In each case if you start with the given temperature and translate it to the other scale you get the same digits you started with, but in a different order.

Funnily enough, the same thing happens for the TOP temperature.

Find THE POST.

[enigma456]

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Here’s a solution using the [[

`SubstitutedExpression()`

]] solver from theenigma.pylibrary.This Python program runs in 97ms.

Run:[ @repl.it ]Solution:THE POST = 546 7235.And

A = 8.The temperatures are:

The are only two possible pairs of 4-digit temperatures with the same digit content in both scales, and only one possible pair of 3-digit temperatures, so once you’ve worked those out it is easy to arrive at the solution.

To save trying to remember whether one adds or subtracts 32, and whether before or after multiplying, I always use the fact that -40° is the same in both scales. So the rule is:

add 40; multiply by 5/9 or 9/5 as appropriate; subtract 40.

Which factor to apply is easy: fewer Celsius degrees are needed to reach boiling point.

I gave up thinking in Fahrenheit over 50 years ago. It amazes me that anyone still uses it.

@geoff: Does this model check that one of HEAT and HOTS is °C and the other is °F?

Given the range of the temperatures I think the following constraint should do it:

Or you can rearrange the clauses of the constraints in lines 39-43 to give a single constraint that selects only valid values:

@Jim: The extra constraint you suggest is stated in the Enigma description, but is probably not strictly essential, as the model gets the single correct answer (and your temperature values) without this extra constraint.