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Algebra Puzzles

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ABCDEF*6=ABCDEF find ABCDEF if A=1.

No solution. x*6 = x only for x=0, which is impossible in your situation above.

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ABCDEF*6=ABCDEF find ABCDEF if A=1.

If A=1 then ABCDEF = BCDEF

Dividing both sides by A we have BCDEF*6 = BCDEF or BCDEF=0

Thus ABCDEF = 0. This is true no matter what value A takes.

If A is nonzero then BCDEF=0. If A=0 ABCDEF=0 by inspection.

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ABCDEF*6=ABCDEF find ABCDEF if A=1.

If A=1 then ABCDEF = BCDEF

Dividing both sides by A we have BCDEF*6 = BCDEF or BCDEF=0

Thus ABCDEF = 0. This is true no matter what value A takes.

If A is nonzero then BCDEF=0. If A=0 ABCDEF=0 by inspection.

We understand the puzzle differently. I interpreted ABCDEF as representing a six-digit number, each digit represented by a letter. In that case, no solution is possible. You seem to have understood ABCDEF to mean A * BCDEF, in which case the only solution is for BCDEF to be zero.

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