CT probably have less of them of though due to the different methods of problem generation. The compositions they use all come from public sources, and CT has considered adding them as an optional side set, but the priority for now has been on only using problems extracted from games. Some of them can be quite practical too, although some more than others, but they are usually interesting calculation exercises none-the-less. This isn't surprising, as after all, compositions are often composed deliberately for their beauty. To be fair, some of the compositions are very nice problems, and would probably be amongst the nicest in their set. The initial set of problems that included compositions were directly inserted in the problem set, and didn't pass through the approver queue, and in fact were probably inserted before the tactics trainer approvers existed. The reason you didn't see them is that the tactics trainer approvers were only being given the new problems coming out of the problem generator. The compositions were there pretty much from the start. All of this on chesstempo for no fee is pretty remarkable. To remedy this I do lots of blitz problems to try and work on my intuition which is helpful. For me, for instance, my standard chesstempo rating is much higher than my blitz, which lets me know that I can brute force and find the tactics by calculation, but I am missing some of the intuition of people around my tactical skill level. This may not sound like a big deal, but it can tell you a lot about your playing strength. Chesstempo allows you to switch and maintain separate rating pools between blitz and standard tactics. also has the problem of duplicates, as I know I've seen quite a few in the few problems I've done there. I believe brute calculation is necessary oftentimes, but the patterns you find in many of these compositions won't ever come up. has many problems which are compositions, and as such are unrealistic brute calculation problems.
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