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Remember that Mega Boards, can supply 200ma power to led at the same time . Each LED consumption is around 20ma, then you can supply about 10 leds for each board.
So, if they all are going to stay ON at the same time, you all need to connect half leds on a board, and the other half, on the other.
Read the Part about Mega Boards... Looks like the 200mA Information is not 100% correct.... It´s true for ONE Ground Pin.... But the Mega got 4 GRD´s
Also, please note that this is absolute maximum rating and exposing the device to absolute maximum conditions for longer duration of time could possibly cause damage to the device.
If you want to "professionally" build your HC you should consider this. It's as you say, the arduinos are cheap so wouldn't it be better to decrease the chance of failure?
By the way: LEDs do light up decently at a lot less current. Low current LEDs only require like 3mA to light up bright enough. It's worth a try.
But the Arduino connects all GND pins of the ATmega. The problem is you can't control the current to each pin regardless which pin of the header you use.
The current will not necessarily be divided evenly between the pins. If you want to make sure nothing breaks you can't use more than 200mA.