If you look at this link, there's a design for lighting a model railroad with LEDs, where a 24V supply drives 7 LEDs in series, with current limited by a single 33 ohm resistor. Nominal current is 100mA. (Note that the circuit is repeated 3 times, so each board has 21 LEDs.)

http://model-railroad-hobbyist.com/node/20523?page=1

I think it's a flawed design. The amount of current that will flow is highly dependent on the voltage of the power supply, along with the voltage drop in each LED. If either of those figures isn't what's expected, the current will change a fair amount. For example, if the drop through each LED is constant, you can expect to see a change in the current of over 10% if the variation in the voltage is 1.5%.

The problem is that the voltage drop is almost all in the diodes, and it's nonlinear, with only the 33 ohm resistor setting the current. I believe the system would be much more robust if there were an LM317 regulator to limit the current, set up with a resistor to form a current-control circuit, a design that's in all the data books. If the desired current is 100mA and the drop from output to adjustment terminal of an LM317 is 1.25V, then it looks as if 12.5 ohms would be the right value.

What do people here think?

 

The total voltage drop across the LM317 and its current setting resistor is about 3V, so you will either need a higher voltage power supply, or fewer LEDs in series. There is quite a bit of variation in the Vf of LEDs, so you almost need to design for the max expected Vf; not the average...

 

You simply noticed a chronic design flaw among beginners. Most of them don't know how to visualize or math out the effect of normal variations. My rule of thumb is to "waste" about 15% to 20% of the available voltage in the resistor. It seems you don't need a rule of thumb because you just demonstrated that you can do the math.

and, yes, a 317 chip can do 100 ma in less than 3.3 volts. Good call.

 

Page 4. Dropout at 100ma is about 1.5V
Regulating voltage is 1.25V
1.5 + 1.25 = 2.75V
Available voltage is 3.3 (nominal).
It will probably work.