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Deduction involves listing the alternative explanations and eliminating all but one

This principle is so basic that I have repeated it, with minor variations, in a number of cases:

It is an old maxim of mine that when you have excluded the impossible, whatever remains, however improbable, must be the truth [BERY].
Eliminate all other factors, and the one which remains must be the truth [SIGN].
--- when you have eliminated, the impossible, whatever remains, however improbable, must be the truth [SIGN].
--- when you have eliminated all which is impossible, whatever remains, however improbable, must be the truth [BLAN].
I now proceeded, using my familiar method of logical analysis, to narrow down the possible solutions [BLAN].
It is impossible as I state it, and therefore I must in some respect have stated it wrong [PRIO].
One should always look for a possible alternative and provide against it [BLAC].
How did you know it was there?
Because I knew it was nowhere else
[SECO].