What functions can be implemented in a single CLB block of XC4000?

[r20de20]

Hi there!

School stuff. I try to learn FPGA and know few things, but it seems I don't quite understand them.

There is this task:
"Can the following logic functions be implemented in a single CLB block of an XC4000 device?"

While I know the answers:
These are possible:
any 5-variable function
any 4-variable function + a specified 5-variable function
a specified 9-variable function
any 4-variable function + a specified 6-variable function
2x any 4-variable function + any 3-variable function

These are not:
3x any 4-variable function
4x any 2-variable function
a specified 10-variable function
any 6-variable function

... I'm not sure of some of them. As per my knowledge, one CLB block of XC4000 consists of 3 LUTs, a mutliplexer and other parts like flip flops, carry. Each LUT has 4 inputs and 1 output.
So it is pretty obvious function with 6 variables wouldn't work, because it has 2^6 = 64 different cases, while LUTs support only 3 * 2^4 = 48 cases. But why is "3x any 4-variable function" impossible to implement? For me it is exactly matching the size of inputs we have available, so it is clear I lack knowledge in this topic. I've tried to research it online and used GPT, but I haven't found any information related to this question.

I kindly ask you for explanation. Thank you in advance for any tips/rules, which would help me in the future.

[CaptDon]

Better to move this to the FPGA forum.

[up8051]

http://xilinx.pe.kr/_xilinx/html/ref/fpga4000.html

Two LUTs are 4 inputs
One LUT is 3 inputs