IBM Ponder This #203 · March 2015

Punched tapes are roll of paper that can be written by punching holes.
All 26 letters of the English alphabet (A-Z) can be encoded using 5-bit wide tape.

How many bits do we need to be able to write twice?

Supply your answer as a 2**X long list of letters, such that using your encoding, one can punch some holes on a blank tape and encode any letter; and then add some more holes (one can not undo a punch) to write any other letter.

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Bonus '*' for those who can fit an intelligible sentence into a correct answer.

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Update (03/04): We have a translation function f from {0,1}^X to {A,B,...,Z} such that for every letter alpha (in A-Z) we can find X bits value x such that f(x)=alpha and for every other letter beta there exists another X bits value y_beta such that f(y_beta)=beta and y_beta>=x bitwise. I.e., every 1 (hole) in x remains a 1 in y_beta, while a 0 in x may be changed to 1 in y_beta ("adding hole"). Note that once you punch beta you are no longer required to remember alpha so y_beta encodes only beta.

Solution

Best opened after a real attempt

To be added.