The basic idea was to create simple circuit with usage transistors, 4000 and 74HC series integrated circuits. I have created 3 bit random number generator with graphical presentation. Below there is logic circuit of this PRNG:

We have here 3 bit shift register which input is feed from XOR gate which is connected to two outputs from this register. It allows to generate number from range 1-7 in according to clock signal. To achieve better random sequence you could use generator based on avalanche noise. Here is example circuit: Random Sequence Generator based on Avalanche Noise.

The XOR gate was created with usage of three gates OR, NAND and AND. Here is logic circuit for this XOR gate:

This XOR gate was implemented with usage of NPN transistors. We need six NPN transistors and nine resistors for create this gate. Below there is schematic of this gate:

Below there is schematic of whole circuit:

We have here CD4047 IC used to generate clock. It is configured to work as astable multivibrator with free running. I have chosen values of resistor R and capacitor C to get in result 9 Hz frequency. This clock drives 74HC164 shift register which is used to generate pseudo random number. Inputs of shift register are connected to output from XOR gate. XOR gate is connected to switch to initiate a number generation because by default all outputs of shift register have LOW value at initial state. I have used a HP 5082-7356 display which have BCD input and allows to latch input value. Because we have 3 bit output from shift register the MSB of BCD input is connected to GND. It allows to display number from range 0 - 7. The button connected to pin number 5 of this display is used to latch a number generated by pseudo random generator. All circuit is powered by 5 volts coming from output of LM7805 linear voltage regulator.

Here is short video presentation of this circuit: