Talk:Three cups problem

Traditional solvable version
Traditionally, the solvable version is solved in three moves, to prevent people from realizing that the solvable version is trivial. That way the deception often goes unnoticed.

the move series is

Flip A and B

Flip A and C

Flip A and B

Then the middle cup is turned face down to give the other person the unsolvable version.

When the other person invariably ends up with them face down again, you turn the middle one up, then solve the solvable version for them, using the mirror image of the solution shown above, then turn the middle face down again. 74.211.58.183 (talk)

Impossibility proof
Why does the proof need to have abstract notation? Additionally, why not just address every case, as it shows the symmetry of the system (up vs down)?

0 cups up → 2 cups up; 1 cups up → {1 or 3} cups up;  2 cups up → {0 or 2} cups up;  3 cups up → 1 cups up

It's then clear that the parity of the cups never changes, and so you can't get from one cup upright to two. 132.199.99.15 (talk) 13:54, 11 February 2014 (UTC)