There are 5 friends, A, B, C, D and E, each of whom makes 2 assertions, so that it is possible for him to tell 2 Truths, or a Truth and Lie, or 2 Lies.

A says:
"Either B or D tells a Truth and a Lie.
Either C or E tells 2 Lies."

B says:
"Either A or C tells a Truth and a Lie.
Either D tells 2 Lies or E tells 2 Truths."

C says:
"Either A or D tells 2 Truths.
Either B tells a Truth and a Lie or E tells 2 Lies."

D says:
"Either A or E tells 2 Lies.
Either B tells 2 Lies or C tells 2 Truths."

E says:
"Either A or B tells 2 Truths.
Either C or D tells a Truth and a Lie."

What is the condition, as to truth-telling and lying, of each of these five painfully-candid friends?
[It is assumed that 'Either p or q' means that either p is the case and q is not; or q is the case and p is not.]


There is an example of a simple and straightforward solution of this puzzle using only mechanical techniques (no intuition) here: http://nbviewer.ipython.org/7076411

It is fascinating to me that the solution (in this case) simply drops out of finding the "standard form" of the puzzle. In other words, once the puzzle is translated into the notation and the redundancies removed its form simply IS the answer.

In contrast, Bricken's article shows how mechanical application of the Bricken Basis results in a simple form that includes both solutions by dint of permitting ambiguity in the form. He says, "The remaining variables are
mutually contingent, which implies that there is more than one solution."

Warm regards,
~Simon