Why would the LEDs have to be broken up like that?
You need to ensure that the sum of the forward voltages of the diodes is less than your supply voltage. Assuming you have something like a 12V supply, 2 blue LEDs will work, three may not. Whilst you can probably put 4 or more red LEDs in series at this voltage, it is far simpler if you have strings of the same size (easiest to ensure a similar brightness) so for 6 LEDs, you can choose 1 string of 6, 2 of 3, 3 or 2 or 6 or 1. The ones which fit the best are as I suggested.
...why wouldn't the LEDs see the full supply voltage?
There will be some voltage drop by the transistors used as the output drivers of the 555. It will be quite low at low currents, but don't bargain on having an *exactly* rail to rail swing. At the currents you'd be looking at, the specs suggest that something between 0.4 and 0.75 volts would be dropped when the output is pulled low, and up to 1.7 volts when pulled high.
See the electrical characteristics on page 4 of the
datasheet.
How would you do it with the transistors? With the MOSFETs?
OK, with mosfets you'd do it like this:
Essentially you do it the same with bipolar transistors, however you need to note that with bipolar transistors both BE junctions are forward biased and separated only by the 2 base resistors. The naive solution tying the bases together and using a single resistor to the 555 will cause massive currents to flow and the sudden death of (probably) both transistors.
I used a separate gate resistor with the mosfets, but it would be possible to eliminate them entirely without any real problems (although gate resistors are required in some cases).