CT #11523
Yes, you are right - I put the correct number in the title, but then botched it in the body (-: So the number should be #11523 not #11423.
CT #20625
On #20625 Fritz wants to play 4...Kd7 for about a minute before switching to 4...QxN The difference in evaluation slowly climbs until after about 5 minutes Fritz shows about 8 pawns difference the same as Toga. It’s difficult to believe that Fritz’s programmers would ever give as high a penalty as 8 pawns for something as insubstantial as king exposure, but Fritz doesn’t see an actual mate until 8.Qd4+ is played when it finds mate in eleven in about 30 seconds or so. So I’m not sure what is happening here either. This is what Fritz is looking at when 4.Nf7+ has been played on the board:
1.Qh7+ Kf8 2.Qh8+ Ke7 3.Qg7+ Kd8 4.Nf7+ Kd7 5.Nxd6+ Kc6 6.Nxe8 Qxe8 7.b5+ Kb6 8.Qd4+ c5 9.bxc6+ Ka6 10.Qc5 bxc6 11.Rb2 Qh5 12.Qxc6+ Ka5 13.Rb5+ Line
Note that 13...Rxh5 wins the black queen, but Fritz won’t admit to having seen that at the stage when 4.Nf7+ has been played.
I’m being strict in marking the problems, because I feel that a good number are already up to the kind of standard that you get in a tactics book. Since you have so many potential problems available it seems to me that it might be feasible to have all the problems up to that standard eventually - so this approach might be more helpful in the long run.
I'm actually a little surprised its rated so low at the moment
Whilst I agree with you about #25045 (but it would greatly benefit from editing to add an extra move), the issue is that it’s possible to use a simple algorithm to solve quite a large percentage of the problems (even more so on CTS), very quickly and with minimal chess benefit: 1) Select all possible captures and checks as your candidate moves 2) If any candidates are checks play the most forcing check, else play the most forcing capture.
Using the above algorithm what would one play in #25045 and #11523? Hmmm, thought so. That’s why this kind of position *needs* the additional moves that justify the obvious first move. IMOP, with the prevalence of this issue on CTS, anyone there with an accuracy stat below about 70% is likely to be making almost exclusive use of the kind of algorithm outlined above and this may explain why there are often plaintive remarks on the message board from people whose practical play has not been improved, despite their prowess on CTS.
My own experience on these two was that although I was able to mentally analyze #25045 out to quiescence quite quickly, I couldn’t see the justification of #11523 (lots of branching) in a reasonable time and had to resort at least partially to the guessing game, but of course it did produce the right answer here!