DAY 25

Comment

It turns out that in this system, X means 'change', O means 'leave unchanged', and 'change' followed by 'change' is equivalent to 'leave unchanged'.
You might, for example, think of a system of push buttons, where X means 'push the button' and O means 'leave the button as it is'; so XOOX, for example, would mean push the 1st and 4th buttons.

Answer

XOOO.

Readers' methods

Clive from Hatfield:
I thought of a row of four light switches, ABCD.
Switch A: click then don't click is click once = X;
switch B: click and click again is the same as don't click = O;
switch C: don't click and still don't click = O;
switch D: identical to switch B.

Stephen E, Durham DH1:
method: Line them up:
XOXX followed by
XOOX makes
OOXO
So following down each column 2Xs makes O, 2Os makes O, and X then O makes X.
Using the same logic:
XXOX followed by
OXOX makes
XOOO.

Gitty H, London N16:
I realized that in the first equation the letters that were the same in the first and second sequence
were marked with 0 whilst the one that was changed was X making the answer 00X0,
therefore i applied this to the second set of sequences - XX0X and 0X0X and got the answer X000.