Lenovo IdeaPad Y50-70-59441231 meets your requirements.
A comprehensive review can be found here.
I am talking about model with GTX 960M. Price: 1499 Euro.
According to your spec:
- NVIDIA GeForce GTX 960M has 4096 MB GDDR5 memory - the same memory bandwidth as the previous GTX 860M, it has higher core clock and it leads to a slightly better performance. 960M is almost 10 percent faster and similar to the desktop GTX 750 Ti. Many games of 2014/2015 can be played fluently in FullHD resolution and high detail settings.
- Memory: up to 16 GB DDR3-1600, dual-channel, two memory banks
- Samsung SSD PM851 512 GB MZ7TE512HMHP, 512 GB. It is less than desired, but it can be easily replaced. Take the price into account - SSD are much more expensive.
- Display: 15.6 inch 16:9, 3840x2160 pixel, Samsung L FLLTN156FL02L01, IPS (glossy)
- There are three USB ports on this notebook, whereas two of them are USB 3.0 ports (Source)
- Numpad: Yes
- Backlight: Yes.
The side shafts of the island-style keys are made of translucent red
plastic, and the light shines through the actual key bodies, rather
than simply leaking from around the key cutouts, as in other backlit
Lenovo's Y50 is explicitly aimed at gamers. Thus,
it is not surprising that it can render all current games smoothly. It
is normally possible to select the Full HD resolution and high to very
high quality settings. The resolution and/or quality level has to be
reduced in some games, for example "The Witcher 3". The frame rates
are only slightly higher than that of laptops equipped with a GeForce
GTX 860M graphics core. However, the advantage over 860 models of the
Y50 is greater, like in the 3DMark benchmarks, because the GeForce GTX
860M GPUs in the Y50 models do not clock at their maximum possible
The screen's maximum resolution (3840 x 2160 pixels) can only be fully
utilized in rare cases. This option is at most possible in games that
only have moderate hardware requirements. The Y50 only achieves just
below 70 fps in the benchmark of the game "Dirt Rally" in very low
quality settings. The rates drop to 25.3 fps in medium and 22.8 fps in
high settings. Source.
Diablo III Reaper of Souls on Lenovo Y50-70 (with 860M).