How to multiplex 8 pieces of 74141 without transistors?
The trick is that you don't multiplex the 74141 parts, you drive them directly from a dedicated driver. You need to store the 4-bit value in some type of memory device, such as a latch, flip-flop, shift register, or more complicated IC. There are a lot of ways to attack the problem, depending on what you're most comfortable with.

Use a 4-bit latch or flip-flop (7475, 7477) to store one digit at a time. Use 8x 4-bit latches, with each clock/enable pin brought out separately.
Use a 4+ bit shift register with parallel outputs (74164) with each chip chained to the next one. Uses only 2-3 Arduino pins, but you must update all digits simultaneously.
Use an I/O expander (MCP23017) and an I2C interface on the Arduino. This allows you to address each digit individually while only needing two pins on the Arduino.