As it turns out, if the Sudoku is a regular puzzle with one solution, if such a pattern is present, the two digits involved in the conjugate pairs should always be removed from the notes of the cell in question. This is true whether there is an odd or even number of such cells—if it is one parity, i.e. odd, the combination may result in a multiple-solution impasse; if it is the other, i.e. even, the digits will be eliminated anyway as solutions are assigned to the other cells in the pseudocycle. In this case, {2,7} would be removed from E1, leaving only {3,5} as the remaining possibilities.
Let's examine the case above more closely: if A1 is 2, then A7 is 7, B8 is 2, and E8 is 7, which eliminates {2,7} from E1 because both digits are already assigned. If you pick 7 for A1, E8 must likewise be 2, also eliminating both digits. Therefore E1 must be reduced to {3,5}. As another example,
- {2,7} in A1 and A7
- {2,7} in A7 and E7
- {2,3,5,7} in E1
If A1 is 2, then A7 is 7 and E7 is also 2, so E1 could be 7. But if A1 is 7, E7 is likewise 7, so E1 could be 2. Now, reducing E1 to {2,7} will not work because the puzzle has only one solution, and doing so would make 2 solutions possible! So we must reduce E1 to {3,5} in this case as well.